rational problem solving definition

What is Problem Solving? (Steps, Techniques, Examples)

By Status.net Editorial Team on May 7, 2023 — 5 minutes to read

What Is Problem Solving?

Definition and importance.

Problem solving is the process of finding solutions to obstacles or challenges you encounter in your life or work. It is a crucial skill that allows you to tackle complex situations, adapt to changes, and overcome difficulties with ease. Mastering this ability will contribute to both your personal and professional growth, leading to more successful outcomes and better decision-making.

Problem-Solving Steps

The problem-solving process typically includes the following steps:

• Identify the issue : Recognize the problem that needs to be solved.
• Analyze the situation : Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present.
• Generate potential solutions : Brainstorm a list of possible solutions to the issue, without immediately judging or evaluating them.
• Evaluate options : Weigh the pros and cons of each potential solution, considering factors such as feasibility, effectiveness, and potential risks.
• Select the best solution : Choose the option that best addresses the problem and aligns with your objectives.
• Implement the solution : Put the selected solution into action and monitor the results to ensure it resolves the issue.
• Review and learn : Reflect on the problem-solving process, identify any improvements or adjustments that can be made, and apply these learnings to future situations.

Defining the Problem

To start tackling a problem, first, identify and understand it. Analyzing the issue thoroughly helps to clarify its scope and nature. Ask questions to gather information and consider the problem from various angles. Some strategies to define the problem include:

• Brainstorming with others
• Asking the 5 Ws and 1 H (Who, What, When, Where, Why, and How)
• Analyzing cause and effect
• Creating a problem statement

Generating Solutions

Once the problem is clearly understood, brainstorm possible solutions. Think creatively and keep an open mind, as well as considering lessons from past experiences. Consider:

• Creating a list of potential ideas to solve the problem
• Grouping and categorizing similar solutions
• Prioritizing potential solutions based on feasibility, cost, and resources required
• Involving others to share diverse opinions and inputs

Evaluating and Selecting Solutions

Evaluate each potential solution, weighing its pros and cons. To facilitate decision-making, use techniques such as:

• SWOT analysis (Strengths, Weaknesses, Opportunities, Threats)
• Decision-making matrices
• Pros and cons lists
• Risk assessments

After evaluating, choose the most suitable solution based on effectiveness, cost, and time constraints.

Implementing and Monitoring the Solution

Implement the chosen solution and monitor its progress. Key actions include:

• Communicating the solution to relevant parties
• Setting timelines and milestones
• Assigning tasks and responsibilities
• Monitoring the solution and making adjustments as necessary
• Evaluating the effectiveness of the solution after implementation

Utilize feedback from stakeholders and consider potential improvements. Remember that problem-solving is an ongoing process that can always be refined and enhanced.

Problem-Solving Techniques

During each step, you may find it helpful to utilize various problem-solving techniques, such as:

• Brainstorming : A free-flowing, open-minded session where ideas are generated and listed without judgment, to encourage creativity and innovative thinking.
• Root cause analysis : A method that explores the underlying causes of a problem to find the most effective solution rather than addressing superficial symptoms.
• SWOT analysis : A tool used to evaluate the strengths, weaknesses, opportunities, and threats related to a problem or decision, providing a comprehensive view of the situation.
• Mind mapping : A visual technique that uses diagrams to organize and connect ideas, helping to identify patterns, relationships, and possible solutions.

Brainstorming

When facing a problem, start by conducting a brainstorming session. Gather your team and encourage an open discussion where everyone contributes ideas, no matter how outlandish they may seem. This helps you:

• Generate a diverse range of solutions
• Encourage all team members to participate
• Foster creative thinking

When brainstorming, remember to:

• Reserve judgment until the session is over
• Encourage wild ideas
• Combine and improve upon ideas

Root Cause Analysis

For effective problem-solving, identifying the root cause of the issue at hand is crucial. Try these methods:

• 5 Whys : Ask “why” five times to get to the underlying cause.
• Fishbone Diagram : Create a diagram representing the problem and break it down into categories of potential causes.
• Pareto Analysis : Determine the few most significant causes underlying the majority of problems.

SWOT Analysis

SWOT analysis helps you examine the Strengths, Weaknesses, Opportunities, and Threats related to your problem. To perform a SWOT analysis:

• List your problem’s strengths, such as relevant resources or strong partnerships.
• Identify its weaknesses, such as knowledge gaps or limited resources.
• Explore opportunities, like trends or new technologies, that could help solve the problem.
• Recognize potential threats, like competition or regulatory barriers.

SWOT analysis aids in understanding the internal and external factors affecting the problem, which can help guide your solution.

Mind Mapping

A mind map is a visual representation of your problem and potential solutions. It enables you to organize information in a structured and intuitive manner. To create a mind map:

• Write the problem in the center of a blank page.
• Draw branches from the central problem to related sub-problems or contributing factors.
• Add more branches to represent potential solutions or further ideas.

Mind mapping allows you to visually see connections between ideas and promotes creativity in problem-solving.

Examples of Problem Solving in Various Contexts

In the business world, you might encounter problems related to finances, operations, or communication. Applying problem-solving skills in these situations could look like:

• Identifying areas of improvement in your company’s financial performance and implementing cost-saving measures
• Resolving internal conflicts among team members by listening and understanding different perspectives, then proposing and negotiating solutions
• Streamlining a process for better productivity by removing redundancies, automating tasks, or re-allocating resources

In educational contexts, problem-solving can be seen in various aspects, such as:

• Addressing a gap in students’ understanding by employing diverse teaching methods to cater to different learning styles
• Developing a strategy for successful time management to balance academic responsibilities and extracurricular activities
• Seeking resources and support to provide equal opportunities for learners with special needs or disabilities

Everyday life is full of challenges that require problem-solving skills. Some examples include:

• Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
• Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
• Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
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Rational Decision Making: The 7-Step Process for Making Logical Decisions

Published: October 17, 2023

Psychology tells us that emotions drive our behavior, while logic only justifies our actions after the fact . Marketing confirms this theory. Humans associate the same personality traits with brands as they do with people  — choosing your favorite brand is like choosing your best friend or significant other. We go with the option that makes us feel something.

But emotions can cloud your reasoning, especially when you need to do something that could cause internal pain, like giving constructive criticism, or moving on from something you’re attached to, like scrapping a favorite topic from your team's content calendar.

There’s a way to suppress this emotional bias, though. It’s a thought process that’s completely objective and data-driven. It's called the rational decision making model, and it will help you make logically sound decisions even in situations with major ramifications , like pivoting your entire blogging strategy.

But before we learn each step of this powerful process, let’s go over what exactly rational decision making is and why it’s important.

What is Rational Decision Making?

Rational decision making is a problem-solving methodology that factors in objectivity and logic instead of subjectivity and intuition to achieve a goal. The goal of rational decision making is to identify a problem, pick a solution between multiple alternatives, and find an answer.

Rational decision making is an important skill to possess, especially in the digital marketing industry. Humans are inherently emotional, so our biases and beliefs can blur our perception of reality. Fortunately, data sharpens our view. By showing us how our audience actually interacts with our brand, data liberates us from relying on our assumptions to determine what our audience likes about us.

Rational Decision Making Model: 7 Easy Steps(+ Examples)

1. Verify and define your problem.

To prove that you actually have a problem, you need evidence for it. Most marketers think data is the silver bullet that can diagnose any issue in our strategy, but you actually need to extract insights from your data to prove anything. If you don’t, you’re just looking at a bunch of numbers packed into a spreadsheet.

To pinpoint your specific problem, collect as much data from your area of need and analyze it to find any alarming patterns or trends.

“After analyzing our blog traffic report, we now know why our traffic has plateaued for the past year — our organic traffic increases slightly month over month but our email and social traffic decrease.”

2. Research and brainstorm possible solutions for your problem.

Expanding your pool of potential solutions boosts your chances of solving your problem. To find as many potential solutions as possible, you should gather plenty of information about your problem from your own knowledge and the internet. You can also brainstorm with others to uncover more possible solutions.

Potential Solution 1: “We could focus on growing organic, email, and social traffic all at the same time."

Potential Solution 2: “We could focus on growing email and social traffic at the same time — organic traffic already increases month over month while traffic from email and social decrease.”

Potential Solution 3: "We could solely focus on growing social traffic — growing social traffic is easier than growing email and organic traffic at the same time. We also have 2 million followers on Facebook, so we could push our posts to a ton of readers."

Potential Solution 4: "We could solely focus on growing email traffic — growing email traffic is easier than growing social and organic traffic at the same time. We also have 250,000 blog subscribers, so we could push our posts to a ton of readers."

Potential Solution 5: "We could solely focus on growing organic traffic — growing organic traffic is easier than growing social and email traffic at the same time. We also just implemented a pillar-cluster model to boost our domain’s authority, so we could attract a ton of readers from Google."

3. Set standards of success and failure for your potential solutions.

Setting a threshold to measure your solutions' success and failure lets you determine which ones can actually solve your problem. Your standard of success shouldn’t be too high, though. You’d never be able to find a solution. But if your standards are realistic, quantifiable, and focused, you’ll be able to find one.

“If one of our solutions increases our total traffic by 10%, we should consider it a practical way to overcome our traffic plateau.”

4. Flesh out the potential results of each solution.

Next, you should determine each of your solutions’ consequences. To do so, create a strength and weaknesses table for each alternative and compare them to each other. You should also prioritize your solutions in a list from best chance to solve the problem to worst chance.

Potential Result 1: ‘Growing organic, email, and social traffic at the same time could pay a lot of dividends, but our team doesn’t have enough time or resources to optimize all three channels.”

Potential Result 2: “Growing email and social traffic at the same time would marginally increase overall traffic — both channels only account for 20% of our total traffic."

Potential Result 3: “Growing social traffic by posting a blog post everyday on Facebook is challenging because the platform doesn’t elevate links in the news feed and the channel only accounts for 5% of our blog traffic. Focusing solely on social would produce minimal results.”

Potential Result 4: “Growing email traffic by sending two emails per day to our blog subscribers is challenging because we already send one email to subscribers everyday and the channel only accounts for 15% of our blog traffic. Focusing on email would produce minimal results.”

Potential Result 5: “Growing organic traffic by targeting high search volume keywords for all of our new posts is the easiest way to grow our blog’s overall traffic. We have a high domain authority, Google refers 80% of our total traffic, and we just implemented a pillar-cluster model. Focusing on organic would produce the most results.”

5. Choose the best solution and test it.

Based on the evaluation of your potential solutions, choose the best one and test it. You can start monitoring your preliminary results during this stage too.

“Focusing on organic traffic seems to be the most effective and realistic play for us. Let’s test an organic-only strategy where we only create new content that has current or potential search volume and fits into our pillar cluster model.”

6. Track and analyze the results of your test.

Track and analyze your results to see if your solution actually solved your problem.

“After a month of testing, our blog traffic has increased by 14% and our organic traffic has increased by 21%.”

7. Implement the solution or test a new one.

If your potential solution passed your test and solved your problem, then it’s the most rational decision you can make. You should implement it to completely solve your current problem or any other related problems in the future. If the solution didn’t solve your problem, then test another potential solution that you came up with.

“The results from solely focusing on organic surpassed our threshold of success. From now on, we’re pivoting to an organic-only strategy, where we’ll only create new blog content that has current or future search volume and fits into our pillar cluster model.”

Avoid Bias With A Rational Decision Making Process

As humans, it’s natural for our emotions to take over your decision making process. And that’s okay. Sometimes, emotional decisions are better than logical ones. But when you really need to prioritize logic over emotion, arming your mind with the rational decision making model can help you suppress your emotion bias and be as objective as possible.

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RATIONAL PROBLEM SOLVING

Introduction

Rational problem solving is an important component of successful decision-making. It involves the use of logical reasoning and critical thinking to determine the best possible solution to a problem. Rational problem solving is a cognitive process that involves analyzing a problem, breaking it down into its component parts, developing possible solutions, evaluating the possible solutions, selecting the best one, and then implementing it. The ability to effectively use rational problem-solving processes is crucial for success in both academic and professional settings.

Rational problem solving is a cognitive process that involves analyzing a problem, breaking it down into its component parts, developing possible solutions, evaluating the possible solutions, selecting the best one, and then implementing it. It is a systematic approach that follows a logical sequence of steps to reach an optimal solution. This process can be broken down into five distinct stages: problem definition, problem analysis, solution generation, solution evaluation, and solution implementation.

Problem Definition

The first step in rational problem solving is to define the problem. This involves identifying the issue and determining its cause. Once the problem has been identified, it is important to consider the context and potential implications of the problem. This step requires an understanding of the objectives and constraints of the problem.

Problem Analysis

The second step in rational problem solving is to analyze the problem. This involves exploring the components of the problem and identifying potential solutions. It is important to consider the resources available and the potential impacts of the various solutions.

Solution Generation

The third step in rational problem solving is to generate potential solutions. This involves brainstorming possible solutions and considering the pros and cons of each. It is important to consider the feasibility and potential costs of each solution.

Solution Evaluation

The fourth step in rational problem solving is to evaluate the solutions. This involves comparing the solutions in terms of their effectiveness, cost, and impact. It is important to consider the potential risks and consequences of each solution.

Solution Implementation

The fifth and final step in rational problem solving is to implement the solution. This involves taking action to implement the chosen solution. It is important to monitor the results of the solution to ensure that it is achieving the desired outcome.

Rational problem solving is an important component of successful decision-making. It involves the use of logical reasoning and critical thinking to determine the best possible solution to a problem. This process requires an understanding of the problem, an analysis of the components of the problem, the generation of potential solutions, the evaluation of the solutions, and then the implementation of the chosen solution. The ability to effectively use rational problem-solving processes is crucial for success in both academic and professional settings.

Bazerman, M. H., & Moore, D. A. (2013). Judgment in managerial decision making. John Wiley & Sons.

Klein, G. (1998). Sources of power: How people make decisions. MIT press.

Simon, H. A. (1996). The sciences of the artificial (Vol. 3). MIT press.

Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185(4157), 1124-1131.

Related terms

Reactive schizophrenia, reality orientation, reading span, receptive aphasia, rebelliousness, reciprocal determinism.

RATIONAL PROBLEM SOLVING

Using correct and logical reasoning to solve a problem

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Problem Solving

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• Seth A. Margolis 3 ,
• Patricia Osborne 3 &
• Jeffrey S. Gonzalez 3 , 4  

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Problem-solving skills training (PSST) ; Problem-solving therapy – primary care (PST-PC) ; Problem-solving therapy – SO (PST-SO) ; Social problem-solving therapy (SPST)

Problem-solving therapy (PST) is a brief, empirically supported, cognitive-behavioral intervention aimed at training clients to identify, evaluate, and resolve everyday problems through the methodical application of problem-solving skills. In addition to teaching specific coping skills, PST emphasizes the importance of maintaining a positive problem-solving orientation and a rational problem-solving style (D’Zurilla & Nezu, 2010 ).

An individual’s problem-solving orientation encompasses how one perceives problems, to what/whom they attribute these problems, how they appraise problematic situations, and the degree to which they view their problems as under their control. A major goal of PST is to help clients view problems as solvable challenges instead of insurmountable impasses.

A person’s problem - solvi...

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References and Readings

Allen, S. M., Shah, A. C., Nezu, A. M., Ciambrone, D., Hogan, J., & Mor, V. (2002). A problem-solving approach to stress reduction among younger women with breast carcinoma: A randomized controlled trial. Cancer, 94 (12), 3089–3100.

Article   PubMed   Google Scholar  

Arean, P. A., Perri, M. G., Nezu, A. M., Schein, R. L., Christopher, F., & Joseph, T. X. (1993). Comparative effectiveness of social problem-solving therapy and reminiscence therapy as treatments for depression in older adults. Journal of Consulting and Clinical Psychology, 61 (6), 1003–1010.

Article   PubMed   CAS   Google Scholar  

Areán, P. A., Raue, P., Mackin, R. S., Kanellopoulos, D., McCulloch, C., & Alexopoulos, G. S. (2010). Problem-solving therapy and supportive therapy in older adults with major depression and executive dysfunction. American Journal of Psychiatry, 167 , 1391–1398.

Catalan, J., Gath, D. H., Anastasiades, P., Bond, S. A., Day, A., & Hall, L. (1991). Evaluation of a brief psychological treatment for emotional disorders in primary care. Psychological Medicine, 21 (4), 1012–1018.

Article   Google Scholar  

Chang, E. C., D’Zurilla, T. J., & Sanna, L. J. (Eds.). (2004). Social problem solving: Theory, research, and training . Washington, DC: American Psychological Association.

Google Scholar  

D’Zurilla, T. J., & Nezu, A. M. (2010). Problem-solving therapy. In K. S. Dobson (Ed.), Handbook of cognitive-behavioral therapies (3rd ed., pp. 197–225). New York: Guilford Press.

Grant, J. S., Elliott, T. R., Weaver, M., Bartolucci, A. A., & Ginger, J. N. (2002). Telephone intervention with family caregivers of stroke survivors after rehabilitation. Stroke, 33 (8), 2060–2065.

Hegel, M. T., Barrett, J. E., & Oxman, T. E. (2000). Training therapists in problem-solving treatment of depressive disorders in primary care: Lessons learned from the “treatment effectiveness project”. Families, Systems, & Health, 18 , 423–435.

Houts, P. S., Nezu, A. M., Nezu, C. M., & Bucher, J. A. (1996). The prepared family caregiver: A problem-solving approach to family caregiver education. Patient Education and Counseling, 27 , 63–73.

Mynors-Wallis, L., & Gath, D. (1997). Predictors of treatment outcome for major depression in primary care. Psychological Medicine, 27 (3), 731–736.

Nezu, A. M., Nezu, C. M., & D’Zurilla, T. J. (2010). Problem-solving therapy. In N. Kazantzis, M. S. Reinecke, & A. Freeman (Eds.), Cognitive and behavioral theories in practice (pp. 76–114). New York: Guilford Press.

Nezu, A. M., Nezu, C. M., Felgoise, S. H., McClure, K. S., & Hots, P. S. (2003). Project genesis: Assessing the efficacy of problem-solving therapy for distressed adult cancer patients. Journal of Consulting and Clinical Psychology, 71 (6), 1036–1048.

Oxman, T. E., Hegel, M. T., Hull, J. G., & Dietrich, A. J. (2008). Problem-solving treatment and coping styles in primary care for minor depression. Journal of Consulting and Clinical Psychology, 76 (6), 933–943.

Perri, M. G., Nezu, A. M., McKelvey, W. F., Shermer, R. L., Renjilian, D. A., & Viegener, B. J. (2001). Individual versus group therapy for obesity: Effects of matching participants to their treatment preferences. Journal of Consulting and Clinical Psychology, 69 (4), 722–726.

Sahler, O. J., Fairclough, D. L., Phipps, S., Mulhern, R. K., Dolgin, M. J., Noll, R. B., et al. (2005). Using problem-solving skills training to reduce negative affectivity in mothers of children with newly diagnosed cancer: Report of a multisite randomized trial. Journal of Consulting and Clinical Psychology, 73 (2), 272–283.

Wade, S. L., Walz, N. C., Carey, J. C., & William, K. M. (2008). Preliminary efficacy of a web-based family problem-solving treatment program for adolescents with traumatic brain injury. Journal of Head Trauma Rehabilitation, 23 (6), 369–377.

Wade, S. L., Wolfe, C., Brown, T. M., & Pestian, J. P. (2005). Putting the pieces together: Preliminary efficacy of a web-based family intervention for children with traumatic brain injury. Journal of Pediatric Psychology, 30 (5), 437–442.

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Margolis, S.A., Osborne, P., Gonzalez, J.S. (2013). Problem Solving. In: Gellman, M.D., Turner, J.R. (eds) Encyclopedia of Behavioral Medicine. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1005-9_208

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Rational Decision-Making Model: Meaning, Importance And Examples

What is the rational decision-making model? Rational decision-making is a method that organizations, businesses and individuals use to make the…

What is the rational decision-making model? Rational decision-making is a method that organizations, businesses and individuals use to make the best decisions. Rational decision-making, one of many decision-making tools, helps users come up with the most suitable course of action. In this blog, we will look at the meaning of rational decision-making, the importance of rational decision-making and study some rational decision-making examples.

Rational decision-making is a process in which decision-makers go through a set of steps and processes and choose the best solution to a problem. These decisions are based on data analysis and logic, eliminating intuition and subjectivity.

Rational decision-making means that every variable factor, every piece of information about all the available options, has been taken into account. 

What Is The Rational Decision-Making Model Used For?

What is the rational decision-making process, non-rational decision making.

The most basic use of the rational decision-making model is to ensure a consistent method of making decisions. This could be used as a standardized decision-making tool across an organization or to ensure that all managers receive the same information to make decisions. The rational decision-making process can be used to maintain a structured, step-by-step approach for every decision.

What Is The Rational Decision-Making Process ?

How the rational decision-making model is implemented can be explained in seven steps:

(There is also an example to help you understand the importance of rational decision-making)

1. Understand and define the scope

Just stating that a problem exists isn’t enough. Solid, accurate data is required to understand and analyze the problem in depth. This lets you know how much attention it requires.

It’s vital to collect as much relevant and accurate data around the problem as possible.

Here’s a rational decision-making example:

Your social media posts aren’t translating to conversions. What could the problem be? Once the analytics reports come in, you realize there isn’t enough engagement. The issue isn’t that your posts are not reaching the right audience, it’s that they don’t engage them. This sets up the next step: figuring out why the problem exists. Why is user engagement low?

2. Research and get feedback

The next step in the rational decision-making process is to delve into the problem. Find out what is causing the problem and how it can be solved. You could start with a brainstorming session and find out what your team thinks.

Rational decision-making example continued:

The budget is good, there are enough views and likes on the posts. So, why is there a lack of engagement? Why aren’t users interacting with the post? Why aren’t they clicking on the CTA?

You might need new types of posts; perhaps the current posts aren’t trendy. Maybe the posts don’t evoke an emotional response from the audience. Or they don’t convey what the product can do for the audience.

Now that you know what the causes could be, you are a step closer. It’s time to collate the data.

The team comes together with their opinions and findings. After a few customer surveys, the major issues are identified as follows:

• Potential consumers don’t know how the product will add value to their lives.
• Potential customers don’t understand the posts’ objectives and aren’t clear on what the product is.

3. List your choices

There are bound to be a host of opinions and innumerable choices about how to address the issue. Consider all of them so that you don’t create more problems later.

This is where you start to use rational decision-making:

Now that the problem has been understood, it’s time to list your options.

You could create a post that showcases what the product does.

You could have an informative GIF that shows that product in action.

You could create additional whitepapers to showcase how the product adds value and thus is beneficial for the customer to buy.

The analytics show that traffic isn’t the issue, so you don’t have to focus on garnering more traffic. Your focus has to be on conversions.

Your color schemes and CTA could be a little more impactful.

Maybe video clips are the way to go?

4. Analyze your options carefully

Now that you have all the options in front of you, cross out the ones that don’t add value or don’t solve the problem. Understand how each of the potential solutions could turn out and what other effects they could have.

Point 6 is about having a back up plan. Once you’ve chosen the plan that is likely to serve you the best, choose the second best option as well. You could use that as your back up, in case things don’t go according to plan.

While it’s great to get a quick solution to a real problem, the solution should be permanent or at least solve the majority of the issue.

The example of the rational decision-making process continued:

This is where you set about deciding the benefits of each of your choices mentioned above.

A video clip post would mean additional costs.

Redesigning the graphics may lead to more views and interaction but dilute your following.

A whitepaper is a good idea, but it doesn’t help with conversions. It’s ideal for customers to click on the CTA.

While GIFs are very popular, the image you choose has to convey the right information and be impactful. You may need to rework the branding for this to work.

While it would be great to have a post that showcases how the product works, it can’t be overly technical.

5. Understand the results you want

This is where the importance of rational decision-making comes into play. Understand what you expect from the solutions. There has to be a clear outcome because of the decision that is made. Knowing what you expect from your actions is important. It’s always a good idea to test the solution to see if it resolves the problem entirely.

Rational decision-making model example continued:

The best course of action might be to assign different teams for the different potential solutions.

One team could create a GIF, while the other works on the video clip and another on the ‘how to use’ post.

Once the teams have all made rough drafts, a productive critiquing session could be conducted. The teams can then look at each others’ solutions and point out the merits and drawbacks of each.

This way a general consensus can be reached and the best option or options can be selected. It is also advisable to use predictive social media tools. There are algorithms and equations that could help predict the success of a post to some degree.

6. Have a backup plan

While this may not always be necessary and can be a little cost-intensive, it may be worthwhile to have a backup plan if the solution doesn’t give you the intended results. This means that you should either have another strategy in place, created using the rational decision-making model .

Even though your plan has been made after careful thought, there is a chance that it either does not go as per plan or that an external factor interferes and throws your plan into chaos.

Try to have a back-up plan to make sure that your business isn’t impacted.

Now that you’ve decided to go with a combination of a GIF and an information-based post, go ahead and begin drafting your white paper as well.

7. Implement

Once the team has done all the work and created the solution, implement it. Implementing this plan means that everyone has to be on board. This means that everyone should be informed and be willing to contribute in executing the plan. The plan won’t work if everyone isn’t working toward the same goal.

As logic and data have been used to reach the decision, it’s likely going to be the most effective one.

Non -Rational Decision-Making

Non-rational decision-making is quite simply the opposite of rational decision-making . Non-rational decision-making is generally used when there isn’t enough information available or when there isn’t enough time to carry out the research and analysis required to employ rational decision-making methods.

Non-rational decision-making can be used when the person or team making the decisions has experienced that issue before or their collective experience allows them to predict what the outcome of their decision would be.

To sum it up, rational decision making can be the difference between a high performance culture driven by results and an unorganized setting. If you would like to drive decisions that guarantee results, you have to employ strategies that kindle organizational objectives based on real data. Let’s sum up the steps explained in this post about the importance of rational decision-making.

• Understand and define the scope
• Research and get feedback
• List your choices
• Analyze your options carefully
• Understand the results you want

Now that you have some idea of what the rational decision-making process is, you may be curious to find out how to make better decisions for your business. To understand more about the importance of rational decision-making , take a look at Harappa’s Making Decisions course. It delves deep into how the best decisions can be reached. The course is for you if you’re looking to get into business and learn how to use rational decision-making.

Explore Harappa Diaries to learn more about topics such as How To Define Problem , Steps involved in Ethical Decision Making , Importance Of Decision Making and How To Overcome Indecisiveness to classify problems and solve them efficiently.

The Ultimate Guide to Rational Decision-Making (With Steps)

Making decisions is an integral part of our lives. However, how many times do we really stop to think whether our choices are rational or not?

This article dives deep into the concept of rational decision-making, its importance, real-life examples, steps involved, factors influencing it, ways to enhance your skills, potential challenges, and how cognitive biases impact it. Let’s dive in.

What is Rational Decision-Making?

Rational decision-making, at its core, is a multi-step process used to make choices that are logical, informed, and objective. It involves identifying a decision problem, gathering information, evaluating alternatives, and selecting the most rational choice. This is a stark contrast to decisions based on subjectivity or intuition, which may often rely on feelings, emotions, or personal biases.

The goal of rational decision-making is to reach decisions that support your objectives in the most optimal way. The basis of this process is rationality—a concept that propels us to make decisions that provide the maximum benefit or, in other words, the best possible outcome. Rationality encourages us to follow a path that aligns with our goals and values while making decisions. It’s an antidote to impulsive choices or decisions clouded by bias and personal emotions.

While intuitive decisions can sometimes lead to effective outcomes, especially in situations demanding quick responses, rational decision-making allows us to consider all available options, analyze their potential consequences, and make an informed choice. This often leads to decisions that are more aligned with our long-term goals and less likely to result in unintended consequences.

Why is Rational Decision-Making Important?

Rational decision-making is the cornerstone of effective problem-solving and critical thinking. It helps us to make informed choices that are not only beneficial but also ethical, a crucial aspect in both personal and professional life.

In business, rational decision-making can lead to strategies that maximize profit, minimize risk, and promote organizational growth. It ensures resource optimization by aligning decisions with business objectives. Rationality ensures that every decision is data-driven, increasing the likelihood of successful outcomes.

On a personal level, rational decision-making can help us make better choices about our health, finances, relationships, and more. It enables us to make choices that align with our values and life goals, improving our overall quality of life.

Examples of Using Rational Decision-Making

Let’s see how rational decision-making manifests in various spheres.

Business: A company looking to launch a new product will employ rational decision-making. They’ll conduct market research, analyze competitor products, evaluate their resources, and predict potential profits before making a decision. This ensures the decision is based on facts and not just intuition.

Leadership: Leaders use rational decision-making while shaping policies or resolving conflicts. A school principal, for instance, may have to decide whether to enforce a strict no-mobile policy.

They’ll consider the pros and cons, consult with teachers, parents, and students, and make a decision that is most beneficial for the school’s academic environment.

Personal Finance: An individual considering their retirement savings plan would utilize rational decision-making. They might begin by understanding the importance of saving for retirement and gathering information about various options like 401(k)s, IRAs, or traditional savings accounts.

They would evaluate these alternatives, considering factors like potential growth, risk level, and tax benefits. The decision would be based on their financial situation, retirement goals, and risk tolerance, ensuring their choice is not impulsive but grounded in careful consideration and analysis.

Steps Involved in Rational Decision-Making

The rational decision-making process comprises several key steps. Here’s a rundown:

1. Identify the Decision

The first step in rational decision-making is acknowledging that a decision is required. The decision is usually a problem but can also be an opportunity. This is the foundational stage where the problem or situation is recognized, and the need for a decision becomes apparent.

You can’t make a rational decision unless you know exactly what the problem is and the context of the decision that needs to be made. Ask yourself questions such as:

• Why does a decision need to be made?
• What consequences will unfold if no decision is made?
• What desired outcome are we aiming for?
• What stands in the way of achieving it?

Take, for instance, a business observing declining profits. The company identifies the problem and realizes that strategic decisions need to be made to address this issue.

It might ask: What is the reason behind the decreasing profits? What will happen if the situation is not addressed? What are our financial goals, and what is impeding us from achieving them? This level of detailed understanding and clarity sets the stage for the subsequent steps of the decision-making process.

2. Gather Information

Once the decision has been identified, the next step is to gather relevant information about it. This could include data analysis, research, consultations with experts, surveys, etc.

Using the previous example, the business might look into financial statements, assess market trends, and consider feedback from customers. A thorough and unbiased collection of data is critical as it forms the backbone of a rational decision.

3. Identify Alternatives

The third step involves generating a list of potential alternatives. There is often more than one way to address a problem or situation, so it’s important to consider different approaches and options.

For the business facing decreasing profits, alternatives could include cost-cutting, investing in new marketing strategies, introducing new products, or even merging with another company. Creativity and open-mindedness are key in this stage to ensure a wide range of options.

4. Evaluate Alternatives

After generating alternatives, the next crucial step is to evaluate each one. This stage involves a systematic analysis of the pros and cons, feasibility, potential impact, and other factors pertinent to each option. Here, establishing your decision criteria—such as cost-effectiveness, scalability, risk level, and potential return—is key. Once established, these criteria need to be weighed based on their importance to solving the problem at hand.

For example, a business might establish criteria like cost, projected return, and alignment with company values. These criteria would be applied to evaluate the potential impact of different marketing strategies, the feasibility of cost-cutting measures, or the implications of a merger.

This systematic evaluation process, underpinned by established and weighted decision criteria, enables a business to compare and contrast different options effectively. It assists in determining which alternative aligns best with the defined criteria and thus holds the highest potential for success.

5. Choose an Alternative

This step involves making the actual decision among the evaluated alternatives. Typically, the best alternative is the one with the greatest likelihood of solving the issue, paired with the lowest degree of risk.

It’s where the business might choose the most cost-effective marketing strategy that is expected to reach the widest audience. While this stage concludes with a decision, the rational decision-making process is not yet complete.

6. Take Action

This is where the chosen alternative is implemented. It involves carrying out the decision and monitoring its progress.

For the business, this would mean launching the selected marketing strategy and keeping a close eye on metrics such as customer engagement, sales, and profit margins. It’s important to remember that this stage might involve overcoming obstacles and making adjustments as necessary.

7. Review the Decision

The final step of the process is to review and evaluate the results of the decision. This includes analyzing whether the decision has resolved the problem or situation and, if not, considering what adjustments need to be made.

In our business example, this could mean assessing whether the new marketing strategy has indeed increased profits. If it hasn’t, the business might need to revisit previous steps of the process to identify and implement a new decision.

These steps make up the backbone of the rational decision-making process, enabling us to systematically approach our choices, ensuring they are backed by logic and evidence.

Assumptions for Using a Rational Decision-Making Model

To effectively utilize the rational decision-making process, it’s necessary to make several key assumptions. These assumptions create a baseline for the decision-making process and help ensure its effective implementation:

• Complete Information: One must assume that all the information needed to make the decision is available and accessible. This includes details about the problem, potential solutions, and their outcomes.
• Decision-Maker Rationality: The person making the decision is assumed to be rational, meaning they are objective, logical, and aim to make the best choice based on the information available.
• Clear Objectives: The decision-maker is assumed to have clear and consistent objectives or goals that guide the decision-making process.
• Time and Resources: It’s assumed that the decision-maker has adequate time and resources to gather information, evaluate alternatives, and make a decision.
• Decision-Maker Independence: The decision-maker is assumed to have the freedom and authority to make the decision without undue influence or restrictions.
• Stable Environment: The environment in which the decision is being made is assumed to be stable, allowing for reliable predictions about the consequences of each alternative.
• Logical Evaluation: It’s assumed that the decision-maker can logically evaluate the pros and cons of each alternative, weigh them against each other, and make a rational choice.

Other Rational Decision-Making Models

While the steps above cover the basics of rational decision-making, there are several rational decision-making models that have been developed by scholars and researchers over the years.

These models provide structured approaches to making decisions based on logical reasoning and analysis. Here are a few examples:

• The Rational Economic Model: This model assumes that individuals make decisions by maximizing their utility or satisfaction, considering all available information, and weighing the costs and benefits of different alternatives.
• The Bounded Rationality Model: Proposed by Herbert Simon, this model recognizes that humans have limitations in processing information and making fully rational decisions. It suggests that individuals make decisions that are “good enough” rather than optimal, taking into account their cognitive constraints and the available information.
• The Normative Decision Model: This model focuses on the ideal decision-making process, providing a step-by-step framework for making rational decisions. It emphasizes gathering complete information, considering all alternatives, and evaluating the potential outcomes before selecting the best option.
• The Garbage Can Model: This model views decision-making as a chaotic process that occurs in organizations. It suggests that decisions often result from a combination of problems, solutions, participants, and circumstances coming together in a “garbage can” and being resolved opportunistically.
• The Prospect Theory: Proposed by Daniel Kahneman and Amos Tversky, this model challenges the assumptions of rational decision-making by considering how individuals assess and weigh potential gains and losses. It suggests that people tend to be risk-averse when it comes to gains but risk-seeking when it comes to losses.

These are just a few examples of rational decision-making models. Each model offers a unique perspective and set of principles for approaching decision-making tasks. The choice of model depends on the context, problem complexity, available information, and the decision-makers preferences and constraints.

Factors Influencing Rational Decision-Making

While the idea of making a completely rational decision sounds perfect, in reality, our decisions are often influenced by various factors.

• Information Availability: The amount and quality of information at our disposal can greatly influence our decisions. With limited or incorrect information, we may end up making less-than-optimal decisions.
• Time Constraints: Often, we are pressed for time while making decisions. Under such constraints, we might not go through the full rational decision-making process.
• Cognitive Limitations: Our cognitive capacity to process information and make decisions is limited. We can be overwhelmed with too many alternatives or complex decision scenarios.
• Emotions: Our emotions often play a part in our decisions. We might make irrational choices under emotional distress.

Impact of Cognitive Biases on Rational Decision-Making

Cognitive biases can seriously impact our rational decision-making abilities. These mental shortcuts or “biases” can lead us to make decisions that are not in our best interest.

For instance, confirmation bias can make us pay more attention to information that confirms our pre-existing beliefs and ignore contradicting evidence. Similarly, the anchoring bias can cause us to rely heavily on the first piece of information we receive when making decisions.

Cognitive biases often lead to irrational choices. Being aware of these biases is the first step towards mitigating their impact on our decision-making process.

Potential Challenges in Rational Decision-Making

Rational decision-making, despite its merits, isn’t without its challenges. Some of these include:

• Information Overload: In an age of data deluge, filtering through massive amounts of information to make decisions can be overwhelming.
• Analysis Paralysis: Overanalyzing or overthinking can lead to indecision or delays in decision-making.
• Unpredictable Outcomes: Even with a thorough analysis, outcomes can be unpredictable due to the dynamic nature of our environment.

Developing Rational Decision-Making Skills

Wondering how to become better at making rational decisions? Here are some tips to get you going:

• Improve Critical Thinking: Critical thinking allows us to objectively analyze information and logically derive conclusions. By developing your critical thinking skills, you can better evaluate decision alternatives.
• Practice Mindfulness: Being aware of your thoughts and emotions can help you identify when they are clouding your decision-making process.
• Use Decision-Making Models: Decision-making models can provide a structured approach to rational decision-making. They can help guide you through complex decision scenarios.

Remember, developing rational decision-making skills takes time and practice. Stay patient and keep practicing.

Frequently Asked Questions

Rational decision-making is a structured, logical process that uses evidence and analysis. Intuitive decision-making relies on instinct and gut feelings.

Yes, rational decision-making can be applied in personal situations like choosing a career, managing finances, or making health-related decisions.

Yes, decision-making models like SWOT analysis, decision trees, or cost-benefit analysis can provide structured approaches to enhance rationality.

Wrapping Up

Rational decision-making is a skill that can transform our personal and professional lives, steering us toward more informed and effective choices. Though challenges exist, with awareness and practice, we can significantly improve our decision-making prowess.

By understanding the nuances of rational decision-making, we not only enhance our decision-making abilities but also become better thinkers, planners, and problem-solvers. Now, isn’t that a step towards a more informed and empowered life?

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7.5: Solving Rational Equations

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Learning Objectives

• Solve rational equations.
• Solve literal equations, or formulas, involving rational expressions.

Solving Rational Equations

A rational equation is an equation containing at least one rational expression. Rational expressions typically contain a variable in the denominator. For this reason, we will take care to ensure that the denominator is not 0 by making note of restrictions and checking our solutions.

Solve rational equations by clearing the fractions by multiplying both sides of the equation by the least common denominator (LCD).

Example \(\PageIndex{1}\)

\(\frac{5}{x}-\frac{1}{3} = \frac{1}{x}\)

We first make a note that \(x≠0\) and then multiply both sides by the LCD, \(3x\):

Check your answer by substituting 12 for x to see if you obtain a true statement.

\(\begin{aligned} \frac{5}{x}-\frac{1}{3} &=\frac{1}{x} \\ \color{black}{\frac{5}{\color{OliveGreen}{12}}}-\frac{1}{3} &=\color{black}{\frac{1}{\color{OliveGreen}{12}}} \\ \frac{5}{12}-\frac{4}{12} &=\frac{1}{12} \\ \frac{1}{12} &=\frac{1}{12}\quad\color{Cerulean}{ \checkmark} \end{aligned}\)

The solution is 12.

After multiplying both sides of the previous example by the LCD, we were left with a linear equation to solve. This is not always the case; sometimes we will be left with a quadratic equation.

Example \(\PageIndex{2}\)

\(2-\frac{1}{x(x+1)}=\frac{3}{x+1}\)

In this example, there are two restrictions, \(x≠0\) and \(x≠−1\). Begin by multiplying both sides by the LCD, \(x(x+1)\).

After distributing and dividing out the common factors, a quadratic equation remains. To solve it, rewrite it in standard form, factor, and then set each factor equal to 0.

\(\begin{array}{rlrl}{2 x+1} & {=0} & {\text { or }} & {x-1=0} \\ {2 x} & {=-1} && {x=1} \\ {x} & {=-\frac{1}{2}}\end{array}\)

Check to see if these values solve the original equation.

\(\begin{array}{c|c}{Check\:x=-\frac{1}{2}}&{Check\:x=1}\\{2-\frac{1}{\color{Cerulean}{(-\frac{1}{2})}\color{black}{(\color{Cerulean}{(-\frac{1}{2})}\color{black}{+1)}}}=\frac{3}{\color{Cerulean}{(-\frac{1}{2})}\color{black}{+1}}}&{2-\frac{1}{\color{Cerulean}{1}\color{black}{(\color{Cerulean}{1}\color{black}{+1)}}=}\frac{3}{\color{Cerulean}{1}\color{black}{+1}}}\\{2-\frac{1}{(-\frac{1}{4})}=\frac{3}{\frac{1}{2}}}&{\frac{4}{2}-\frac{1}{2}=\frac{3}{2}}\\{2+1\cdot\frac{4}{1}=3\cdot\frac{2}{1}}&{\frac{3}{2}=\frac{3}{2}}\quad\color{Cerulean}{\checkmark}\\{2+4=6}\\{6=6}\quad\color{Cerulean}{\checkmark} \end{array}\)

The solutions are \(-\frac{1}{2}\) and \(1\).

Up to this point, all of the possible solutions have solved the original equation. However, this may not always be the case. Multiplying both sides of an equation by variable factors may lead to extraneous solutions, which are solutions that do not solve the original equation. A complete list of steps for solving a rational equation is outlined in the following example.

Example \(\PageIndex{3}\)

\(\frac{x}{x+2}+\frac{2}{x^{2}+5 x+6}=\frac{5}{x+3}\)

Step 1 : Factor all denominators and determine the LCD.

\(\begin{aligned} \frac{x}{x+2}+\frac{2}{x^{2}+5 x+6} &=\frac{5}{x+3} \\ \frac{x}{(x+2)}+\frac{2}{(x+2)(x+3)} &=\frac{5}{(x+3)} \end{aligned}\)

The LCD is \((x+2)(x+3)\).

Step 2 : Identify the restrictions. In this case, they are \(x≠−2\) and \(x≠−3\).

Step 3 : Multiply both sides of the equation by the LCD. Distribute carefully and then simplify.

\(\begin{aligned}\color{Cerulean}{(x+2)(x+3)}\color{black}{\cdot}\left(\frac{x}{(x+2)}+\frac{2}{(x+2)(x+3)} \right)&=\color{Cerulean}{(x+2)(x+3)}\color{black}{\cdot\frac{5}{(x+3)}}\\ \frac{x\cdot\color{Cerulean}{\cancel{(x+2)}(x+3)}}{\color{Cerulean}{\cancel{\color{black}{(x+2)}}}}\color{black}{+}\frac{2\cdot\color{Cerulean}{\cancel{(x+2)}\cancel{(x+3)}}}{\color{Cerulean}{\cancel{\color{black}{(x+2)}}\cancel{\color{black}{(x+3)}}}}&\color{black}{=}\frac{5\cdot\color{Cerulean}{(x+2)\cancel{(x+3)}}}{\color{Cerulean}{\cancel{\color{black}{(x+3)}}}}\\x(x+3)+2&=5(x+2)\\x^{2}+3x+2&=5x+10 \end{aligned}\)

Step 4 : Solve the resulting equation. Here the result is a quadratic equation. Rewrite it in standard form, factor, and then set each factor equal to \(0\).

\(\begin{array}{cc}{x+2=0} & {\text { or } \quad x-4=0} \\ {x=-2} & {x=4}\end{array}\)

Step 5 : Check for extraneous solutions. Always substitute into the original equation, or the factored equivalent. In this case, choose the factored equivalent to check:

\(\frac{x}{(x+2)}+\frac{2}{(x+2)(x+3)}=\frac{5}{(x+3)}\)

\(\begin{array}{c|c}{Check\:x=-2}&{Check\:x=4}\\{\frac{-2}{(\color{Cerulean}{-2}\color{black}{+2)}}+\frac{2}{(\color{Cerulean}{-2}\color{black}{+2)(}\color{Cerulean}{-2}\color{black}{+3)}}=\frac{5}{(\color{Cerulean}{-2}\color{black}{+3)}}}&{\frac{4}{(\color{Cerulean}{4}\color{black}{+2)}}+\frac{2}{(\color{Cerulean}{4}\color{black}{+2)(}\color{Cerulean}{4}\color{black}{+3)}}=\frac{5}{(\color{Cerulean}{4}\color{black}{+3)}}}\\{-\frac{2}{0}+\frac{2}{0(1)}=\frac{5}{1}\quad\color{red}{x}}&{\frac{4}{6}+\frac{2}{6\cdot7}=\frac{5}{7}}\\{Undefined\:terms!}&{\frac{2}{3}+\frac{1}{21}=\frac{5}{7}}\\{}&{\frac{14}{21}+\frac{1}{21}=\frac{5}{7}}\\{}&{\frac{15}{21}=\frac{5}{7}}\\{}&{\frac{5}{7}=\frac{5}{7}\quad\color{Cerulean}{\checkmark}} \end{array}\)

Here \(−2\) is an extraneous solution and is not included in the solution set. It is important to note that \(−2\) is a restriction.

The solution is \(4\).

If this process produces a solution that happens to be a restriction, then disregard it as an extraneous solution.

Exercise \(\PageIndex{1}\)

Sometimes all potential solutions are extraneous, in which case we say that there is no solution to the original equation. In the next two examples, we demonstrate two ways in which a rational equation can have no solutions.

Example \(\PageIndex{4}\)

\(\frac{3 x}{x^{2}-4}-\frac{2}{x+2}=\frac{1}{x+2}\)

To identify the LCD, first factor the denominators.

\(\begin{aligned} \frac{3 x}{x^{2}-4}-\frac{2}{x+2} &=\frac{1}{x+2} \\ \frac{3 x}{(x+2)(x-2)}-\frac{2}{(x+2)} &=\frac{1}{(x+2)} \end{aligned}\)

Multiply both sides by the least common denominator (LCD), \((x+2)(x−2)\), distributing carefully.

The equation is a contradiction and thus has no solution.

No solution, \(∅\)

Example \(\PageIndex{5}\)

\(\frac{x}{x-4}-\frac{4}{x+5}=\frac{36}{x^{2}+x-20}\)

First, factor the denominators.

\(\frac{x}{(x-4)}-\frac{4}{(x+5)}=\frac{36}{(x-4)(x+5)}\)

Take note that the restrictions are \(x≠4\) and \(x≠−5\). To clear the fractions, multiply by the LCD, \((x−4)(x+5)\).

\(\begin{array}{cc}{x-4=0}&{ \text { or } }&{ x+5=0} \\ {x=4} && {x=-5}\end{array}\)

Both of these values are restrictions of the original equation; hence both are extraneous.

No solution, \(\emptyset\)

Exercise \(\PageIndex{2}\)

\(\emptyset\)

It is important to point out that this technique for clearing algebraic fractions only works for equations. Do not try to clear algebraic fractions when simplifying expressions. As a reminder, we have

\(\begin{array}{cc} {\color{Cerulean}{Expression}}&{\color{Cerulean}{Equation}}\\{\frac{1}{x}+\frac{x}{2 x+1}}&{\frac{1}{x}+\frac{x}{2 x+1}=0} \end{array}\)

Expressions are to be simplified and equations are to be solved. If we multiply the expression by the LCD, \(x(2x+1)\), we obtain another expression that is not equivalent.

\(\begin{array}{c|c}{\color{red}{Incorrect}}&{\color{Cerulean}{Correct}}\\{\frac{1}{x}+\frac{x}{2x+1}}&{\frac{1}{x}+\frac{x}{2x+1}=0}\\{\neq\color{red}{x(2x+1)}\color{black}{\cdot\left(\frac{1}{x}+\frac{x}{2x+1} \right) }}&{\color{Cerulean}{x(2x+1)}\color{black}{\cdot\left(\frac{1}{x}+\frac{x}{2x+1} \right)}\color{black}{=}\color{Cerulean}{x(2x+1)}\color{black}{\cdot 0}}\\{=2x+1+x^{2}\quad\color{red}{x}}&{2x+1+x^{2}=0}\\{}&{x^{2}+2x+1=0\quad\color{Cerulean}{\checkmark}}\end{array}\)

Literal Equations

Literal equations, or formulas, are often rational equations. Hence the techniques described in this section can be used to solve for particular variables. Assume that all variable expressions in the denominator are nonzero.

Example \(\PageIndex{6}\)

Solve for \(x\):

\(x=\frac{x-5}{y}\)

The goal is to isolate x . Assuming that y is nonzero, multiply both sides by y and then add \(5\) to both sides.

\(x=y z+5\)

Example \(\PageIndex{7}\)

Solve for \(c\):

\(\frac{1}{c}=\frac{1}{a}+\frac{1}{b}\)

In this example, the goal is to isolate \(c\). We begin by multiplying both sides by the LCD, \(a⋅b⋅c\), distributing carefully.

\(\begin{aligned} \frac{1}{c} &=\frac{1}{a}+\frac{1}{b} \\ \color{Cerulean}{a b c}\color{black}{ \cdot \frac{1}{c}} &\color{black}{=}\color{Cerulean}{a b c}\color{black}{ \cdot \frac{1}{a}+}\color{Cerulean}{a b c}\color{black}{ \cdot \frac{1}{b}} \\ a b &=b c+a c \end{aligned}\)

On the right side of the equation, factor out \(c\).

\(a b=c(b+a)\)

Next, divide both sides of the equation by the quantity \((b+a)\).

\(\begin{array}{c}{\frac{a b}{\color{Cerulean}{(b+a)}}\color{black}{=\frac{c(b+a)}{\color{Cerulean}{(b+a)}}}} \\ {\frac{a b}{b+a}=c}\end{array}\)

\(c=\frac{a b}{b+a}\)

Exercise \(\PageIndex{3}\)

Solve for \(y\):

\(x=\frac{y+1}{y−1}\)

\(y=\frac{1+x}{x-1}\)

Key Takeaways

• Begin solving rational equations by multiplying both sides by the LCD. The resulting equivalent equation can be solved using the techniques learned up to this point.
• Multiplying both sides of a rational equation by a variable expression introduces the possibility of extraneous solutions. Therefore, we must check the solutions against the set of restrictions. If a solution is a restriction, then it is not part of the domain and is extraneous.
• When multiplying both sides of an equation by an expression, distribute carefully and multiply each term by that expression.
• If all of the resulting solutions are extraneous, then the original equation has no solutions.

Exercise \(\PageIndex{4}\) Rational Equations

• \(\frac{1}{2}+\frac{1}{x}=\frac{1}{8}\)
• \(\frac{1}{3}−\frac{1}{x}=\frac{2}{9}\)
• \(\frac{1}{3x}−\frac{2}{3}=\frac{1}{x}\)
• \(\frac{2}{5x}−\frac{1}{x}=\frac{3}{10}\)
• \(\frac{1}{2 x+1}=5\)
• \(\frac{3}{3x−1}+4=5\)
• \(\frac{2 x-3}{x+5}=\frac{2}{x+5}\)
• \(\frac{5x}{2x−1}=\frac{x−1}{2x−1}\)
• \(\frac{5}{x−7}=\frac{6}{x−9}\)
• \(\frac{5}{x+5}=\frac{3}{x+1}\)
• \(\frac{x}{6}-\frac{6}{x}=0\)
• \(\frac{5x+x}{5}=−2\)
• \(\frac{x}{x+12}=\frac{2}{x}\)
• \(\frac{2x}{x+5}=\frac{1}{6−x}\)
• \(\frac{1}{x}+\frac{x}{2x+1}=0\)
• \(\frac{9x}{3x−1}−\frac{4}{x}=0\)
• \(1−\frac{2}{x}=\frac{48}{x^{2}}\)
• \(2−\frac{9}{x}=\frac{5}{x^{2}}\)
• \(1+\frac{12}{x}=\frac{12}{x-2}\)
• \(1−\frac{3x−5}{x(3x−4)}=−\frac{1}{x}\)
• \(\frac{x}{2}=\frac{14}{x+3}\)
• \(\frac{3x}{2}=\frac{x+1}{3−x}\)
• \(6=\frac{−3x+3}{x−1}\)
• \(\frac{1}{2x−2}=2+\frac{6(4−x)}{x−2}\)
• \(2+\frac{2x}{x−3}=\frac{3(x−1)}{x−3}\)
• \(\frac{x}{x−1}+\frac{1}{6x−1}=\frac{x(x−1)}{(6x−1)}\)
• \(\frac{12}{x^{2}−81}=\frac{1}{x+9}−\frac{2}{x−9}\)
• \(\frac{14}{x^{2}−49}=\frac{2}{x−7}−\frac{3}{x+7}\)
• \(\frac{6x}{x+3}+\frac{4}{x−3}=\frac{3x}{x^{2}−9}\)
• \(\frac{3x}{x+2}−\frac{17}{x−2}=−\frac{48}{x^{2}−4}\)
• \(x^{-1}+3=0\)
• \(4^{−y}−1=0\)
• \(y^{−2}−4=0\)
• \(9 x^{-2}-1=0\)
• \(3(x−1)^{−1}+5=0\)
• \(5−2(3x+1)^{−1}=0\)
• \(3+2x^{−3}=2x^{−3}\)
• \(\frac{1}{x}=\frac{1}{x+1}\)
• \(\frac{x}{x+1}=\frac{x+1}{x}\)
• \(\frac{3x−1}{3x}=\frac{x}{x+3}\)
• \(\frac{4x−7}{x−5}=\frac{3x−2}{x−5}\)
• \(\frac{x}{x^{2}−9}=\frac{1}{x−3}\)
• \(\frac{3x+4}{x−8}−\frac{2}{8−x}=1\)
• \(\frac{1}{x}=\frac{6}{x(x+3)}\)
• \(\frac{3}{x}=\frac{1}{x+1}+\frac{13}{x(x+1)}\)
• \(\frac{x}{x−1}−\frac{3}{4x−1}=\frac{9x}{(4x-1)(x−1)}\)
• \(\frac{1}{x−4}+\frac{x}{x−2}=2x^{2}−6x+8 \)
• \(\frac{x}{x−5}+\frac{x−1}{x^{2}−11x+30}=\frac{5}{x−6}\)
• \(\frac{x}{x+1}−\frac{6}{5x^{2}+4x−1}=−\frac{5}{5x−1}\)
• \(\frac{−8x^{2}−4}{x−12}+\frac{2(x+2)}{x^{2}+4x−60}=\frac{1}{x+2}\)
• \(\frac{x}{x+2}-\frac{20}{x^{2}-6-x}=\frac{-4}{x-3}\)
• \(\frac{x+7}{x−1}+\frac{x−1}{x+1}=\frac{4}{x^{2}−1}\)
• \(\frac{x−1}{x−3}+\frac{x−3}{x−1}=−\frac{x+5}{x−3}\)
• \(\frac{x−2}{x−5}−\frac{x−5}{x−2}=\frac{8−x}{x−5}\)
• \(\frac{x+7}{x−2}−\frac{81}{x^{2}+5x−14}=\frac{9}{x+7}\)
• \(\frac{x}{x−6}+1=\frac{5x+30}{36−x^{2}}\)
• \(\frac{2x}{x+1}−\frac{4}{4x−3}=−\frac{7}{4x^{2}+x−3}\)
• \(\frac{x−5}{x−10}+\frac{5}{x−5}=−\frac{5x}{x^{2}−15x+50}\)
• \(\frac{5}{x^{2}+5 x+4}+\frac{x+1}{x^{2}+3 x-4}=\frac{5}{x^{2}-1}\)
• \(\frac{1}{x^{2}−2x−63}+\frac{x−9x^{2}+10}{x+21}=\frac{1}{x^{2}−6x−27}\)
• \(\frac{4}{x^{2}-4}+\frac{2(x-2)}{x^{2}-4 x-12}=\frac{x+2}{x^{2}-8 x+12}\)
• \(\frac{x+2}{x^{2}−5x+4}+\frac{x+2}{x^{2}+x−2}=\frac{x−1}{x^{2}−2x−8}\)
• \(\frac{6 x}{x-1}-\frac{11 x+1}{2 x^{2}-x-1}=\frac{6 x}{2 x+1}\)
• \(\frac{8x}{2x−3}+\frac{4x^{2}}{x^{2}−7x+6}=\frac{1}{x−2}\)

1. \(−\frac{8}{3}\)

3. \(−1\)

5. \(−\frac{2}{5}\)

7. \(\frac{5}{2}\)

9. \(−3\)

11. \(-6, 6\)

13. \(−4, 6\)

15. \(−1\)

17. \(−6, 8\)

19. \(−4, 6\)

21. \(−7, 4\)

23. \(∅\)

25. \(∅\)

27. \(−39\)

29. \(\frac{4}{3}, \frac{3}{2}\)

31. \(−\frac{1}{3}\)

33. \(−\frac{1}{2}, \frac{1}{2}\)

35. \(\frac{2}{5}\)

37. \(∅\)

39. \(−\frac{1}{2}\)

41. \(∅\)

43. \(−7\)

47. \(−1\)

49. \(∅\)

51. \(−4\)

53. \(\frac{5}{3}\)

55. \(∅\)

57. \(\frac{1}{2}\)

59. \(−6, 4\)

63. \(\frac{1}{3}\)

Exercise \(\PageIndex{5}\) Literal Equations

Solve for the indicated variable.

• Solve for \(r\): \(t=\frac{D}{r}\)
• Solve for \(b\): \(h=\frac{2A}{b}\)
• Solve for \(P\): \(t=\frac{I}{Pr}\)
• Solve for \(π\): \(r=\frac{C}{2π}\)
• Solve for \(c\): \(\frac{1}{a}=\frac{1}{b}+\frac{1}{c}\)
• Solve for \(y\): \(m=\frac{y−y_{1}}{x−x_{1}}\)
• Solve for \(w\): \(P=2(l+w)\)
• Solve for \(t\): \(A=P(1+rt)\)
• Solve for \(m\): \(s=\frac{1}{n+m}\)
• Solve for \(S\): \(h=S2πr−r\)
• Solve for \(x\): \(y=\frac{x}{x+2}\)
• Solve for \(x\): \(y=2x+15x\)
• Solve for \(R\): \(\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}\)
• Solve for \(S_{1}\): \(\frac{1}{f}=\frac{1}{S_{1}}+\frac{1}{S_{2}}\)

1. \(r=\frac{D}{t}\)

3. \(P=\frac{I}{tr}\)

5. \(c=\frac{ab}{b−a}\)

7. \(w=\frac{P}{2}-l\)

9. \(m=\frac{1}{s}-n\)

11. \(x=-\frac{2y}{y-1}\)

13. \(R=\frac{R_{1}R_{2}}{R_{1}+R_{2}}\)

Exercise \(\PageIndex{6}\) Discussion Board

• Explain why multiplying both sides of an equation by the LCD sometimes produces extraneous solutions.
• Explain the connection between the technique of cross multiplication and multiplying both sides of a rational equation by the LCD.
• Explain how we can tell the difference between a rational expression and a rational equation. How do we treat them differently?

1. Answers may vary

3. Answers may vary

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What Is Creative Problem-Solving & Why Is It Important?

• 01 Feb 2022

One of the biggest hindrances to innovation is complacency—it can be more comfortable to do what you know than venture into the unknown. Business leaders can overcome this barrier by mobilizing creative team members and providing space to innovate.

There are several tools you can use to encourage creativity in the workplace. Creative problem-solving is one of them, which facilitates the development of innovative solutions to difficult problems.

Here’s an overview of creative problem-solving and why it’s important in business.

Access your free e-book today.

What Is Creative Problem-Solving?

Research is necessary when solving a problem. But there are situations where a problem’s specific cause is difficult to pinpoint. This can occur when there’s not enough time to narrow down the problem’s source or there are differing opinions about its root cause.

In such cases, you can use creative problem-solving , which allows you to explore potential solutions regardless of whether a problem has been defined.

Creative problem-solving is less structured than other innovation processes and encourages exploring open-ended solutions. It also focuses on developing new perspectives and fostering creativity in the workplace . Its benefits include:

• Finding creative solutions to complex problems : User research can insufficiently illustrate a situation’s complexity. While other innovation processes rely on this information, creative problem-solving can yield solutions without it.
• Adapting to change : Business is constantly changing, and business leaders need to adapt. Creative problem-solving helps overcome unforeseen challenges and find solutions to unconventional problems.
• Fueling innovation and growth : In addition to solutions, creative problem-solving can spark innovative ideas that drive company growth. These ideas can lead to new product lines, services, or a modified operations structure that improves efficiency.

Creative problem-solving is traditionally based on the following key principles :

1. Balance Divergent and Convergent Thinking

Creative problem-solving uses two primary tools to find solutions: divergence and convergence. Divergence generates ideas in response to a problem, while convergence narrows them down to a shortlist. It balances these two practices and turns ideas into concrete solutions.

2. Reframe Problems as Questions

By framing problems as questions, you shift from focusing on obstacles to solutions. This provides the freedom to brainstorm potential ideas.

3. Defer Judgment of Ideas

When brainstorming, it can be natural to reject or accept ideas right away. Yet, immediate judgments interfere with the idea generation process. Even ideas that seem implausible can turn into outstanding innovations upon further exploration and development.

4. Focus on "Yes, And" Instead of "No, But"

Using negative words like "no" discourages creative thinking. Instead, use positive language to build and maintain an environment that fosters the development of creative and innovative ideas.

Creative Problem-Solving and Design Thinking

Whereas creative problem-solving facilitates developing innovative ideas through a less structured workflow, design thinking takes a far more organized approach.

Design thinking is a human-centered, solutions-based process that fosters the ideation and development of solutions. In the online course Design Thinking and Innovation , Harvard Business School Dean Srikant Datar leverages a four-phase framework to explain design thinking.

The four stages are:

• Clarify: The clarification stage allows you to empathize with the user and identify problems. Observations and insights are informed by thorough research. Findings are then reframed as problem statements or questions.
• Ideate: Ideation is the process of coming up with innovative ideas. The divergence of ideas involved with creative problem-solving is a major focus.
• Develop: In the development stage, ideas evolve into experiments and tests. Ideas converge and are explored through prototyping and open critique.
• Implement: Implementation involves continuing to test and experiment to refine the solution and encourage its adoption.

Creative problem-solving primarily operates in the ideate phase of design thinking but can be applied to others. This is because design thinking is an iterative process that moves between the stages as ideas are generated and pursued. This is normal and encouraged, as innovation requires exploring multiple ideas.

Creative Problem-Solving Tools

While there are many useful tools in the creative problem-solving process, here are three you should know:

Creating a Problem Story

One way to innovate is by creating a story about a problem to understand how it affects users and what solutions best fit their needs. Here are the steps you need to take to use this tool properly.

1. Identify a UDP

Create a problem story to identify the undesired phenomena (UDP). For example, consider a company that produces printers that overheat. In this case, the UDP is "our printers overheat."

2. Move Forward in Time

To move forward in time, ask: “Why is this a problem?” For example, minor damage could be one result of the machines overheating. In more extreme cases, printers may catch fire. Don't be afraid to create multiple problem stories if you think of more than one UDP.

3. Move Backward in Time

To move backward in time, ask: “What caused this UDP?” If you can't identify the root problem, think about what typically causes the UDP to occur. For the overheating printers, overuse could be a cause.

Following the three-step framework above helps illustrate a clear problem story:

• The printer is overused.
• The printer overheats.
• The printer breaks down.

You can extend the problem story in either direction if you think of additional cause-and-effect relationships.

4. Break the Chains

By this point, you’ll have multiple UDP storylines. Take two that are similar and focus on breaking the chains connecting them. This can be accomplished through inversion or neutralization.

• Inversion: Inversion changes the relationship between two UDPs so the cause is the same but the effect is the opposite. For example, if the UDP is "the more X happens, the more likely Y is to happen," inversion changes the equation to "the more X happens, the less likely Y is to happen." Using the printer example, inversion would consider: "What if the more a printer is used, the less likely it’s going to overheat?" Innovation requires an open mind. Just because a solution initially seems unlikely doesn't mean it can't be pursued further or spark additional ideas.
• Neutralization: Neutralization completely eliminates the cause-and-effect relationship between X and Y. This changes the above equation to "the more or less X happens has no effect on Y." In the case of the printers, neutralization would rephrase the relationship to "the more or less a printer is used has no effect on whether it overheats."

Even if creating a problem story doesn't provide a solution, it can offer useful context to users’ problems and additional ideas to be explored. Given that divergence is one of the fundamental practices of creative problem-solving, it’s a good idea to incorporate it into each tool you use.

Brainstorming

Brainstorming is a tool that can be highly effective when guided by the iterative qualities of the design thinking process. It involves openly discussing and debating ideas and topics in a group setting. This facilitates idea generation and exploration as different team members consider the same concept from multiple perspectives.

Hosting brainstorming sessions can result in problems, such as groupthink or social loafing. To combat this, leverage a three-step brainstorming method involving divergence and convergence :

• Have each group member come up with as many ideas as possible and write them down to ensure the brainstorming session is productive.
• Continue the divergence of ideas by collectively sharing and exploring each idea as a group. The goal is to create a setting where new ideas are inspired by open discussion.
• Begin the convergence of ideas by narrowing them down to a few explorable options. There’s no "right number of ideas." Don't be afraid to consider exploring all of them, as long as you have the resources to do so.

Alternate Worlds

The alternate worlds tool is an empathetic approach to creative problem-solving. It encourages you to consider how someone in another world would approach your situation.

For example, if you’re concerned that the printers you produce overheat and catch fire, consider how a different industry would approach the problem. How would an automotive expert solve it? How would a firefighter?

Be creative as you consider and research alternate worlds. The purpose is not to nail down a solution right away but to continue the ideation process through diverging and exploring ideas.

Continue Developing Your Skills

Whether you’re an entrepreneur, marketer, or business leader, learning the ropes of design thinking can be an effective way to build your skills and foster creativity and innovation in any setting.

If you're ready to develop your design thinking and creative problem-solving skills, explore Design Thinking and Innovation , one of our online entrepreneurship and innovation courses. If you aren't sure which course is the right fit, download our free course flowchart to determine which best aligns with your goals.

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Course: Algebra 2   >   Unit 10

Rational equations intro.

• Equations with rational expressions
• Equations with rational expressions (example 2)
• Rational equations
• Finding inverses of rational functions
• Find inverses of rational functions

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Video transcript