Lesson 9 | Equations and Inequalities | 7th Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

7.EE.B.4.B — 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.

Expressions and Equations

7.EE.B.4.B — 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.

Foundational Standards

The foundational standards covered in this lesson

6.EE.B.5

Expressions and Equations

6.EE.B.5 — Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
6.EE.B.8

Expressions and Equations

6.EE.B.8 — Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Criteria for Success

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

Write inequalities to represent word problems, paying attention to the use of inequality symbol.
Solve inequalities in the form $${px+q>r }$$ or $${px+q<r}$$ and $${p(x+q)>r}$$ or $${p(x+q)<r}$$.
Interpret solutions to inequalities in context of the situations they represent (MP.2).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

In this lesson, students will solve inequalities in which the coefficient of the variable is positive. Multiplying and dividing with negative values in inequalities will be addressed in Lesson 10.

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Anchor Problems

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

Problem 1

On Saturday, Bianca has $50 on her debit card when she goes out with some friends. She uses her debit card to spend $14.50 on lunch. She and her friends would like to go to see a movie, but some of her friends are out of money. If the movie tickets cost $6.50 each, how many tickets can Bianca buy without overdrawing on her debit card?

a. Write an expression that represents the total expenses Bianca pays for on Saturday, based on the number of movie tickets she buys.

b. Use your expression to determine how much Bianca spends if she buys 2 tickets, 3 tickets, and 7 tickets.

c. Write an inequality to represent the situation and solve it to answer the question.

Guiding Questions

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Problem 2

Identical copies of books are being packaged and shipped to a bookstore. There are 18 boxes of books that each weigh 31 pounds. The boxes have space for some more books to be added; however, the total weight of all of the boxes cannot exceed 615 pounds. Two workers, Kevin and Olivia, want to determine how many more pounds of books they can add into each box without going over the weight limit.

Kevin writes the inequality $${18(x+31)\geq 615}$$.
Olivia writes the inequality $${18(x+31)\leq 615}$$.

Who wrote the correct inequality? How many extra pounds can they add to each box?

Guiding Questions

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Problem 3

Solve and graph the solution to each inequality below.

a. $${{2\over3} (x-15)>-24}$$

b. $${-1.6+3x \leq 8}$$

Guiding Questions

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Problem Set

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

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Target Task

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

Grace has $105 to buy a cake and pizza for her cousin’s birthday party. She knows she needs to set aside $25 for the cake, and the rest of the money she can spend on pizzas. Each pizza costs $9.25. How many pizzas can Grace afford to buy?

a. Write and solve an inequality to answer the question.

b. Each pizza serves 4 people. If 22 people reply that they will attend the party, how many pizzas should Grace buy? Explain your reasoning.

Student Response

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Additional Practice

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.

EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic B > Lesson 13 — Exercises 1-2, Problem Set
Open Up Resources Grade 7 Unit 6 Practice Problems — Lesson 13
Illustrative Mathematics Sports Equipment Set
Kuta Software Free Pre-Algebra Worksheets Two-Step Inequalities — Do not include problems with negative coefficients for the variable.

Lesson 8

Lesson 10

Lesson Map

Topic A: Solving and Modeling with Equations

Solve one-step equations with rational numbers.

7.EE.B.4.A

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

7.EE.B.4.A

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

7.EE.B.4.A

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

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 2).

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

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

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

Topic B: Solving and Modeling with Inequalities

Solve and graph one-step inequalities.

7.EE.B.4.B

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

7.EE.B.4.B

Solve inequalities with negative coefficients.

7.EE.B.4.B

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

7.EE.B.4.B

Model with inequalities.

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

Equations and Inequalities

Objective

Common Core Standards

Core Standards

Expressions and Equations

Foundational Standards

Expressions and Equations

Expressions and Equations

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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