# Lesson 9

Solutions of Inequalities

Let’s think about the solutions to inequalities.

### Problem 1

1. Select all numbers that are solutions to the inequality $$k > 5$$.

4

5

6

5.2

5.01

0.5

2. Draw a number line to represent this inequality.

### Problem 2

A sign on the road says: “Speed limit, 60 miles per hour.”

1. Let $$s$$ be the speed of a car. Write an inequality that matches the information on the sign.
2. Draw a number line to represent the solutions to the inequality.
3. Could 60 be a value of $$s$$? Explain your reasoning.

### Problem 3

One day in Boston, MA, the high temperature was 60 degrees Fahrenheit, and the low temperature was 52 degrees.

1. Write one or more inequalities to describe the temperatures $$T$$ that are between the high and low temperature on that day.
2. Show the possible temperatures on a number line.

### Problem 4

Select all the true statements.

A:

$$\text-5 < |\text-5|$$

B:

$$|\text-6| < \text-5$$

C:

$$|\text-6| < 3$$

D:

$$4 < |\text-7|$$

E:

$$|\text-7| < |\text-8|$$

(From Unit 7, Lesson 7.)

### Problem 5

Match each equation to its solution.

1. $$x^4=81$$
2. $$x^2=100$$
3. $$x^3=64$$
4. $$x^5=32$$
• 2
• 3
• 4
• 10
(From Unit 6, Lesson 15.)

### Problem 6

1. The price of a cell phone is usually $250. Elena’s mom buys one of these cell phones for$150. What percentage of the usual price did she pay?

2. Elena’s dad buys another type of cell phone that also usually sells for \$250. He pays 75% of the usual price. How much did he pay?

(From Unit 3, Lesson 14.)