Illustrative Mathematics Grade 7, Unit 6, Lesson 13: Reintroducing Inequalities

Learning Targets:

  • I can explain what the symbols ≤ and ≥ mean.
  • I can represent an inequality on a number line.
  • I understand what it means for a number to make an inequality true.

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Illustrative Math
Grade 7

Lesson 13: Reintroducing Inequalities

Let’s work with inequalities.

Illustrative Math Unit 7.6, Lesson 13 (printable worksheets)

Lesson 13 Summary

The following diagram shows how to represent an inequality on a number line and what it means for a number to make an inequality true.
Percent Example

Lesson 13.1 Greater Than One

The number line shows values of x that make the inequality x > 1 true.

  1. Select all the values of x from this list that make the inequality x > 1 true.
    a. 3
    b. -3
    c. 1
    d. 700
    e. 1.95
  2. Name two more values of x that are solutions to the inequality.

Lesson 13.2 The Roller Coaster

A sign next to a roller coaster at an amusement park says, “You must be at least 60 inches tall to ride.” Noah is happy to know that he is tall enough to ride.

  1. Noah is x inches tall. Which of the following can be true: x > 0, x = 6, or x < 0? Explain how you know.
  2. Noah’s friend is 2 inches shorter than Noah. Can you tell if Noah’s friend is tall enough to go on the ride? Explain or show your reasoning.
  3. List one possible height for Noah that means that his friend is tall enough to go on the ride, and another that means that his friend is too short for the ride.
  4. On the number line below, show all the possible heights that Noah’s friend could be.
  5. Noah’s friend is y inches tall. Use and any of the symbols <, =, > to express this height.

Lesson 13.3 Is the Inequality True or False?

The table shows four inequalities and four possible values for x. Decide whether each value makes each inequality true, and complete the table with “true” or “false.” Discuss your thinking with your partner. If you disagree, work to reach an agreement.

Are you ready for more?

Find an example of an inequality used in the real world and describe it using a number line.

Lesson 13 Practice Problems

  1. For each inequality, find two values for x that make the inequality true and two values that make it false.
    a. x + 3 > 70
    b. x + 3 < 70
    c. -5x < 2
    d. 5x < 2
  2. Here is an inequality: -3x > 18.
    a. List some values for x that would make this inequality true.
    b. How are the solutions to the inequality -3 ≥ 18 different from the solutions to -3 ≥ 18? Explain your reasoning.
  3. Match each sentence with the inequality that could represent the situation.
    A. Han got $2 from Clare, but still has less than $20.
    B. Mai spent $2 and has less than $20.
    C. If Tyler had twice the amount of money he has, he would have less than $20.
    D. If Priya had half the money she has, she would have less than $20.
  4. Here are the prices for cheese pizza at a certain pizzeria:
    a. You had a coupon that made the price of a large pizza $13.00. For what percent off was the coupon?
    b. Your friend purchased a medium pizza for $10.31 with a 30% off coupon. What is the price of a medium pizza without a coupon?
    c. Your friend has a 15% off coupon and $10. What is the largest pizza that your friend can afford, and how much money will be left over after the purchase?
  5. Select all the stories that can be represented by the diagram.
    A. Andre studies 7 hours this week for end-of-year exams. He spends 1 hour on English and an equal number of hours each on math, science, and history.
    B. Lin spends $3 on 7 markers and a $1 pen.
    C. Diego spends $1 on 7 stickers and 3 marbles.
    D. Noah shares 7 grapes with 3 friends. He eats 1 and gives each friend the same number of grapes.
    E. Elena spends $7 on 3 notebooks and a $1 pen.

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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