Equations and Inequalities

Lesson 9


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


  • 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


  • 6.EE.B.5

  • 6.EE.B.8

Criteria for Success


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

Tips for Teachers


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


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? 

  1. Write an expression that represents the total expenses Bianca pays for on Saturday, based on the number of movie tickets she buys.
  2. Use your expression to determine how much Bianca spends if she buys 2 tickets, 3 tickets, and 7 tickets.
  3. 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


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Target Task


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? 

  1. Write and solve an inequality to answer the question. 
  2. Each pizza serves 4 people. If 22 people reply that they will attend the party, how many pizzas should Grace buy? Explain your reasoning.

Mastery Response


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