# Lesson 14

Finding Solutions to Inequalities in Context

### Problem 1

The solution to $$5-3x > 35$$ is either $$x>\text-10$$ or $$\text-10>x$$. Which solution is correct? Explain how you know.

### Solution

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### Problem 2

The school band director determined from past experience that if they charge $$t$$ dollars for a ticket to the concert, they can expect attendance of $$1000-50t$$. The director used this model to figure out that the ticket price needs to be \$8 or greater in order for at least 600 to attend. Do you agree with this claim? Why or why not?

### Solution

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### Problem 3

Which inequality is true when the value of $$x$$ is -3?

A:

$$\text-x -6 < \text-3.5$$

B:

$$\text-x- 6 >3.5$$

C:

$$\text-x -6 > \text-3.5$$

D:

$$x -6 > \text-3.5$$

### Solution

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(From Unit 6, Lesson 13.)

### Problem 4

Draw the solution set for each of the following inequalities.

1. $$x\leq5$$

2. $$x<\frac52$$

### Solution

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(From Unit 6, Lesson 13.)

### Problem 5

Write three different equations that match the tape diagram.

### Solution

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(From Unit 6, Lesson 3.)

### Problem 6

A baker wants to reduce the amount of sugar in his cake recipes. He decides to reduce the amount used in 1 cake by $$\frac12$$ cup. He then uses $$4\frac12$$ cups of sugar to bake 6 cakes.

1. Describe how the tape diagram represents the story.
2. How much sugar was originally in each cake recipe?

### Solution

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(From Unit 6, Lesson 2.)

### Problem 7

One year ago, Clare was 4 feet 6 inches tall. Now Clare is 4 feet 10 inches tall. By what percentage did Clare’s height increase in the last year?

### Solution

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(From Unit 4, Lesson 12.)