# Lesson 17

Number of Solutions in One-Variable Equations

- Let's look at the number of solutions an equation may have.

### 17.1: Notice and Wonder: Three Graphs

What do you notice? What do you wonder?

### 17.2: How Many Answers?

How many values of \(x\) make each equation true?

- \(3x + 1 = 10\)
- \(2x + 12 = 2x + 10 + 2\)
- \(2x = x + 2\)
- \(3(x+4) = 3x + 4\)
- \(\frac{2x+6}{2} = x + 6\)
- \(0 = 0\)
- \(x + 3x - 4 = 7(x - \frac{4}{7})\)
- \(0 = 6\)

With your partner, discuss what you notice about the equations based on the number of solutions they have.

### 17.3: Write, Trade, Check

- Write an equation that has either 1, 0, or infinite solutions.
- Trade your equation with your partner. Solve the equation you are given and determine the number of solutions.
- Take turns explaining your reasoning with your partner.
- Repeat the process with a new equation.