# 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.

\(x+x+x = 1+1+1+1+1+1\)

\(x \boldcdot x \boldcdot x = 6\)

\(3x = 6\)

\(x + 3 = 6\)

\(x \boldcdot x \boldcdot x = 1 \boldcdot 1 \boldcdot 1 \boldcdot 1 \boldcdot 1 \boldcdot 1\)

### Problem 2

Write an equation to represent each hanger.

### Problem 3

- Write an equation to represent the hanger.

- Explain how to reason with the hanger to find the value of \(x\).

- 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.

- \(12-m=4\)
- \(12=4\boldcdot m\)
- \(m-4=12\)
- \(\frac{m}{4}=12\)

### Problem 6

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

- \(x=2\frac13\)
- \(x=4\frac15\)
- \(x=\frac76\)

### 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.

- 25%
- 75%
- 125%