# Lesson 7

Reasoning about Solving Equations (Part 1)

Let’s see how a balanced hanger is like an equation and how moving its weights is like solving the equation.

### Problem 1

Explain how the parts of the balanced hanger compare to the parts of the equation.

\(7=2x+3\)

### Problem 2

For the hanger below:

- Write an equation to represent the hanger.
- Draw more hangers to show each step you would take to find \(x\). Explain your reasoning.
- Write an equation to describe each hanger you drew. Describe how each equation matches its hanger.

### Problem 3

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.