# Lesson 10

Interpreting Inequalities

### Problem 1

There is a closed carton of eggs in Mai's refrigerator. The carton contains $$e$$ eggs and it can hold 12 eggs.

1. What does the inequality $$e < 12$$ mean in this context?

2. What does the inequality $$e > 0$$ mean in this context?

3. What are some possible values of $$e$$ that will make both $$e < 12$$ and $$e > 0$$ true?

### Problem 2

Here is a diagram of an unbalanced hanger.

1. Write an inequality to represent the relationship of the weights. Use $$s$$ to represent the weight of the square in grams and $$c$$ to represent the weight of the circle in grams.
2. One red circle weighs 12 grams. Write an inequality to represent the weight of one blue square.
3. Could 0 be a value of $$s$$? Explain your reasoning.

### Problem 3

1. Jada is taller than Diego. Diego is 54 inches tall (4 feet, 6 inches). Write an inequality that compares Jada’s height in inches, $$j$$, to Diego’s height.

2. Jada is shorter than Elena. Elena is 5 feet tall. Write an inequality that compares Jada’s height in inches, $$j$$, to Elena’s height.

### Solution

(From Unit 7, Lesson 8.)

### Problem 4

Tyler has more than \$10. Elena has more money than Tyler. Mai has more money than Elena. Let $$t$$ be the amount of money that Tyler has, let $$e$$ be the amount of money that Elena has, and let $$m$$ be the amount of money that Mai has. Select all statements that are true:

A:

$$t < j$$

B:

$$m > 10$$

C:

$$e > 10$$

D:

$$t > 10$$

E:

$$e > m$$

F:

$$t < e$$

### Problem 5

Which is greater, $$\frac {\text{-}9}{20}$$ or -0.5? Explain how you know. If you get stuck, consider plotting the numbers on a number line.

### Solution

(From Unit 7, Lesson 3.)

### Problem 6

Select all the expressions that are equivalent to $$\left(\frac{1}{2}\right)^3$$.

A:

$$\frac{1}{2} \boldcdot \frac{1}{2} \boldcdot \frac{1}{2}$$

B:

$$\frac{1}{2^3}$$

C:

$$\left(\frac{1}{3}\right)^2$$

D:

$$\frac{1}{6}$$

E:

$$\frac{1}{8}$$