Lesson 13
Reintroducing Inequalities
Let’s work with inequalities.
Problem 1
For each inequality, find two values for \(x\) that make the inequality true and two values that make it false.
- \(x+3>70\)
- \(x+3<70\)
- \(\text-5x<2\)
- \(5x<2\)
Problem 2
Here is an inequality: \(\text-3x > 18\).
- List some values for \(x\) that would make this inequality true.
- How are the solutions to the inequality \(\text-3x \geq 18\) different from the solutions to \(\text-3x > 18\)? Explain your reasoning.
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 |
-
You had a coupon that made the price of a large pizza $13.00. For what percent off was the coupon?
-
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?
-
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?
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.](https://cms-im.s3.amazonaws.com/gHX3tPPhQEtnHhbdamxoTMCV?response-content-disposition=inline%3B%20filename%3D%227-7.6.A4.newPP.02.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.A4.newPP.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162709Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b16f325de4a3c9802976701875281e3dee331957ada4e97f73c32e4a450d3a43)
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.
Lin spends $3 on 7 markers and a $1 pen.
Diego spends $1 on 7 stickers and 3 marbles.
Noah shares 7 grapes with 3 friends. He eats 1 and gives each friend the same number of grapes.
Elena spends $7 on 3 notebooks and a $1 pen.