Lesson 13

Reintroducing Inequalities

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Problem 1

For each inequality, find two values for \(x\) that make the inequality true and two values that make it false.

  1. \(x+3>70\)
  2. \(x+3<70\)
  3. \(\text-5x<2\)
  4. \(5x<2\)

Solution

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Problem 2

Here is an inequality: \(\text-3x > 18\).

  1. List some values for \(x\) that would make this inequality true.
  2. How are the solutions to the inequality \(\text-3x \geq 18\) different from the solutions to \(\text-3x > 18\)? Explain your reasoning.

Solution

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Problem 3

Here are the prices for cheese pizza at a certain pizzeria:

pizza size price in dollars
small 11.60
medium
large 16.25

  1. You had a coupon that made the price of a large pizza $13.00. For what percent off was the coupon?

  2. 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?

  3. 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?

Solution

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(From Unit 4, Lesson 12.)

Problem 4

Select all the stories that can be represented by the diagram.

Tape diagram, 3 equal parts labeled x, one small part colored blue, labeled 1, total 7.
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.

Solution

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(From Unit 6, Lesson 4.)