# Lesson 8

Reasoning about Solving Equations (Part 2)

### Problem 1

Here is a hanger:

1. Write an equation to represent the hanger.
2. Solve the equation by reasoning about the equation or the hanger. Explain your reasoning. ### Solution

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### 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 ### Solution

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### Problem 3

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

### Solution

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(From Unit 4, Lesson 11.)

### 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. 1. What value for $$x$$ can be found using the diagram?
2. Show how to fix Clare’s diagram to correctly match the equation.
3. Use the new diagram to find a correct value for $$x$$.
4. Explain the mistake Clare made when she drew her diagram.

### Solution

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(From Unit 6, Lesson 3.)