# 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?

How many values of $$x$$ make each equation true?

1. $$3x + 1 = 10$$
2. $$2x + 12 = 2x + 10 + 2$$
3. $$2x = x + 2$$
4. $$3(x+4) = 3x + 4$$
5. $$\frac{2x+6}{2} = x + 6$$
6. $$0 = 0$$
7. $$x + 3x - 4 = 7(x - \frac{4}{7})$$
8. $$0 = 6$$

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