1. OBJECTIVE
I will solve absolute-value equations using inverse operations.

2. Rule
| ax + b | = c
MEANS
ax + b = c OR ax + b = -c

3. Solving an Absolute-Value Equation
Solve | x + 5 | = 3
x is positive x is negative
| x + 5 | = 3 | x + 5 | = 3
x + 5 = 3 x + 5 = -3
x = x = -8
x = -2 and -8
Check

4. Solving an Absolute-Value Equation
Solve | x - 2 | + 4 = 7
First, isolate the absolute-value on one side.
x is positive x is negative
| x - 2 | + 4 = 7 | x - 2 | + 4 = 7
| x - 2 | = 3 | x - 2 | = 3
x - 2 = 3 x - 2 = -3
x = x = -1
x = 5 and -1
Check

5. Guided Practice
- | x - 9 | = -5
| x + 24 | - 12 = 43

6. Independent Practice | x + 10 | = 17 | x - 4 | = 12 - | x - 17 | = -42