lesson 7 homework practice solving inequalities

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Course: 7th grade   >   Unit 6

• Plotting inequalities on a number line
• Inequality from graph
• Plotting inequalities
• Testing solutions to inequalities

One-step inequalities examples

• One-step inequalities: -5c ≤ 15
• One-step inequalities
• One-step inequality word problem
• One-step inequalities review

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Video transcript

Solving Inequalities

New york state common core math algebra i, module 1, lesson 14.

Lesson 14 Student Outcomes Students learn if-then moves using the addition and multiplication properties of inequality to solve inequalities and graph the solution sets on the number line. Properties of Inequality Recall the Properties of Inequality:

Addition property of inequality:

If A > B, then A + c > B + c for any real number c.

Multiplication property of inequality:

If A > B, then kA > kB for any positive real number k.

Exit Ticket

1. Find the solution set to each inequality. Express the solution in set notation and graphically on the number line. a. 6x + 2 < 7x - 1

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Solving Inequalities by Multiplying and Dividing Worksheets

How to Solve Inequalities by Multiplying and Dividing - We all know what equations are in mathematics. Equations are a combination of constant values, variables, arithmetic operations, and an equals-to sign. When the equals-to sign is replaced with a "less than," "less than or equal to," "greater than," or "greater than or equal to sign," we call it an inequality. Solving an inequality is very much similar to solving an equation. When you know how to solve an equation, you will know exactly how to solve an inequality. So, how to solve inequalities by multiplying and dividing? Remember how you solved equations by multiplying and dividing? No? Let's recall it. Consider the following equation: 3x=21. To solve this equation, you divide both sides of the equation by 3; 3x/3 = 21/3, x = 7. Now, consider another example; x/3 = 2. To solve this equation, you multiply both sides of the equation by; x/3 × 3 = 2 × 3, x = 6. Now that we have recalled the solving equations, we can move towards solving inequalities. Consider the following example; 4x ≥ 10/3. To solve this inequality, you have to divide the whole inequality with 4; 4x/4 ≥ 10/(3×4), x = 5/6. The only difference between solving inequality and an equation is, when you multiply an inequality with a negative number, the sign of the inequality changes. If the equation had been; -4x ≤ 10/3, we would have multiplied both sides of the inequality with -1/4. -4x × -1/4 ≥ 10/3× - 1/4. Did you see how the sign changed? Well, this is how you solve an inequality through multiplication and division.

Basic Lesson

Demonstrates how to transfer numbers in multiplication and division based equations. We focus on combining like terms and then moving to the free side. Practice problems are provided.

Intermediate Lesson

Explains how to rewrite equations to solve inequalities. Practice problems are provided.

Independent Practice 1

Contains 20 Solving Inequalities by Multiplying and Dividing problems. The answers can be found below.

Independent Practice 2

Features another 20 Solving Inequalities by Multiplying and Dividing problems.

Homework Worksheet

12 Solving Inequalities by Multiplying and Dividing problems for students to work on at home. Example problems are provided and explained.

10 Solving Inequalities by Multiplying and Dividing problems. A math scoring matrix is included.

Homework and Quiz Answer Key

Answers for the homework and quiz.

Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

Where Does the Word "Algebra" Come From?

The word "algebra" comes from the title of a work on mathematics by an Arab mathematician. Al-Khuwarizmi wrote the piece titled Al-gabr. The first mathematician to use letters to represent unknown quantities was French; his name was Francois Viete.

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Grade 7 - Expressions & Equations

Standard 7.EE.B.4b - Simplify one step linear inequalities.

Included Skills:

Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

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Chapter 1, Lesson 5: Solving Inequalities

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Curriculum  /  Math  /  7th Grade  /  Unit 4: Equations and Inequalities  /  Lesson 4

Equations and Inequalities

Lesson 4 of 12

Criteria for Success

Tips for teachers, anchor problems, problem set, target task, additional practice.

Solve equations in the forms $${px+q=r }$$  and $${p(x+q)=r}$$  algebraically.

Common Core Standards

Core standards.

The core standards covered in this lesson

Expressions and Equations

7.EE.B.4.A — Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Foundational Standards

The foundational standards covered in this lesson

6.EE.B.7 — Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Understand that an equation is a statement of balance, and in solving the equation, the balance must be maintained.
• Understand solving an equation as a process of undoing operations using inverse operations that adhere to arithmetic properties. 
• Solve equations in the forms $$px+q=r$$   and $$p(x+q)=r$$ .

Suggestions for teachers to help them teach this lesson

In this lesson, students learn the concepts behind the mechanics of solving an equation. In the next two lessons, students will have further opportunities to practice solving equations in contextual situations. Solving equations in these two forms is a fluency expectation in 7th grade. See our Guide to Procedural Skill and Fluency for ideas of activities to use throughout the lesson and remaining part of the unit.

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

A balance is shown below.

a.   Describe how you can use the balance to find the value of $$x$$ .

b.   Write an equation to represent the situation shown in the balance. 

c.   Use the equation to model the actions you did in part A with the balance.

d.   Repeat parts A–C using the balance shown below.

Guiding Questions

Yoshiro has a new puppy. She decides to create an enclosure for her puppy in her backyard. The enclosure is in the shape of a hexagon, with one pair of opposite sides running the same distance along the length of two parallel flowerbeds. A sketch of the enclosure is shown below. 

If the perimeter of the enclosure is 137 feet, what is the length of each side that runs along the flowerbed, labeled $$n$$ in the diagram? Write an equation to represent the situation, and solve using algebraic properties. 

Grade 7 Mathematics > Module 2 > Topic C > Lesson 22 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds . © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US  license. Accessed Dec. 2, 2016, 5:15 p.m..

Solve the equations:

a.    $${12(x-2)=72}$$

b.    $${- {1\over3}x+4=-2}$$

c.    $${5.6-2p=13}$$

A set of suggested resources or problem types that teachers can turn into a problem set

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Solve each equation for the variable. Show every step in your work that maintains the balance in each equation.

a.    $${{1\over2}(x+8)=-10}$$

b.    $${-5x+12=20}$$

Student Response

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

• Open Up Resources Grade 7 Unit 6 Practice Problems — Lessons 7 and 8, skip review questions
• EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic C > Lesson 22 — Exercises 1-5, Problem Set
• Kuta Software Free Pre-Algebra Worksheets Two-Step Equations Containing Integers
• Kuta Software Free Algebra 1 Worksheets Two-Step Equations
• Algebra By Example 3.1 Solving 1 and 2 Step Equations
• SolveMe Mobiles — These can be done on the computer, or screen shots can be taken and added to a problem set; stick to one-variable mobiles. Also find good challenges here.

Topic A: Solving and Modeling with Equations

Solve one-step equations with rational numbers.

Represent equations in the forms $${px+q=r}$$ and $${p(x+q)=r}$$ using tape diagrams.

Solve equations in the forms $${px+q=r}$$   and $${p(x+q)=r}$$  using tape diagrams.

7.EE.B.3 7.EE.B.4.A

Solve word problems leading to equations in the forms $${px+q=r}$$   and $${p(x+q)=r}$$ (Part 1).

Solve word problems leading to equations in the forms $${px+q=r}$$ and $${p(x+q)=r }$$  (Part 2).

Model with equations in the form $${px+q=r}$$ and $${p(x+q)=r}$$ .

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Topic B: Solving and Modeling with Inequalities

Solve and graph one-step inequalities.

Write and solve inequalities in the forms $${px+q>r}$$  or  $${px+q<r}$$   and $${p(x+q)>r }$$  or $${p(x+q)<r.}$$

Solve inequalities with negative coefficients.

Solve word problems leading to inequalities in the forms $${px+q>r}$$   or $${px+q<r}$$   and $${p(x+q)>r}$$ or $${p(x+q)<r}$$ .

Model with inequalities.

7.EE.B.3 7.EE.B.4.B

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