# Lesson 14

Finding Solutions to Inequalities in Context

The practice problem answers are available at one of our IM Certified Partners

### 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.

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? ### 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\$

(From Grade7, Unit 6, Lesson 13.)

### Problem 4

Draw the solution set for each of the following inequalities.

1. $$x\leq5$$

2. $$x<\frac52$$

(From Grade7, Unit 6, Lesson 13.)

### Problem 5

Write three different equations that match the tape diagram.

(From Grade7, 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?
(From Grade7, 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?

(From Grade7, Unit 4, Lesson 12.)