# Lesson 16

Interpreting Inequalities

### Problem 1

Priya looks at the inequality $$12-x>5$$ and says “I subtract a number from 12 and want a result that is bigger than 5. That means that the solutions should be values of $$x$$ that are smaller than something.”

Do you agree with Priya? Explain your reasoning and include solutions to the inequality in your explanation.

### Solution

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### Problem 2

When a store had sold $$\frac25$$ of the shirts that were on display, they brought out another 30 from the stockroom. The store likes to keep at least 150 shirts on display. The manager wrote the inequality $$\frac35x+30 \geq 150$$ to describe the situation.

1. Explain what $$\frac35$$ means in the inequality.
2. Solve the inequality.

3. Explain what the solution means in the situation.

### Solution

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### Problem 3

You know $$x$$ is a number less than 4. Select all the inequalities that must be true.

A:

$$x<2$$

B:

$$x+6<10$$

C:

$$5x<20$$

D:

$$x-2>2$$

E:

$$x<8$$

### Solution

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(From Unit 6, Lesson 13.)

### Problem 4

Here is an unbalanced hanger.

1. If you knew each circle weighed 6 grams, what would that tell you about the weight of each triangle? Explain your reasoning.
2. If you knew each triangle weighed 3 grams, what would that tell you about the weight of each circle? Explain your reasoning.

### Solution

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(From Unit 6, Lesson 13.)

### Problem 5

Match each sentence with the inequality that could represent the situation.

### Solution

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(From Unit 6, Lesson 13.)

### Problem 6

At a skateboard shop:

1. The price tag on a shirt says $12.58. Sales tax is 7.5% of the price. How much will you pay for the shirt? 2. The store buys a helmet for$19.00 and sells it for $31.50. What percentage was the markup? 3. The shop pays workers$14.25 per hour plus 5.5% commission. If someone works 18 hours and sells \$250 worth of merchandise, what is the total amount of their paycheck for this pay period? Explain or show your reasoning.

### Solution

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(From Unit 4, Lesson 12.)