# Lesson 8

Reasoning about Solving Equations (Part 2)

Let’s use hangers to understand two different ways of solving equations with parentheses.

### Problem 1

Here is a hanger:

- Write an equation to represent the hanger.
- Solve the equation by reasoning about the equation or the hanger. Explain your reasoning.

### Problem 2

Explain how each part of the equation \(9=3(x+2)\) is represented in the hanger.

- \(x\)
- 9
- 3
- \(x+2\)
- \(3(x+2)\)
- the equal sign

### Problem 3

Select the word from the following list that best describes each situation.

### Problem 4

Clare drew this diagram to match the equation \(2x+16=50\), but she got the wrong solution as a result of using this diagram.

- What value for \(x\) can be found using the diagram?
- Show how to fix Clare’s diagram to correctly match the equation.
- Use the new diagram to find a correct value for \(x\).
- Explain the mistake Clare made when she drew her diagram.