# Lesson 3

Staying in Balance

Let's use balanced hangers to help us solve equations.

### Problem 1

Select all the equations that represent the hanger.

A:

$$x+x+x = 1+1+1+1+1+1$$

B:

$$x \boldcdot x \boldcdot x = 6$$

C:

$$3x = 6$$

D:

$$x + 3 = 6$$

E:

$$x \boldcdot x \boldcdot x = 1 \boldcdot 1 \boldcdot 1 \boldcdot 1 \boldcdot 1 \boldcdot 1$$

### Problem 2

Write an equation to represent each hanger.

### Problem 3

1. Write an equation to represent the hanger.

2. Explain how to reason with the hanger to find the value of $$x$$.

3. Explain how to reason with the equation to find the value of $$x$$.

### Problem 4

Andre says that $$x$$ is 7 because he can move the two 1s with the $$x$$ to the other side.

Do you agree with Andre? Explain your reasoning.

### Problem 5

Match each equation to one of the diagrams.

1. $$12-m=4$$
2. $$12=4\boldcdot m$$
3. $$m-4=12$$
4. $$\frac{m}{4}=12$$
(From Unit 6, Lesson 1.)

### Problem 6

The area of a rectangle is 14 square units. It has side lengths $$x$$ and $$y$$. Given each value for $$x$$, find $$y$$.

1. $$x=2\frac13$$
2. $$x=4\frac15$$
3. $$x=\frac76$$
(From Unit 4, Lesson 13.)

### Problem 7

Lin needs to save up \$20 for a new game. How much money does she have if she has saved each percentage of her goal. Explain your reasoning.

1. 25%
2. 75%
3. 125%
(From Unit 3, Lesson 11.)