1. Ch 6.6 Solving Absolute-Value Equations
Objective:
To solve absolute value equations in one variable

2. Definitions
Absolute-Value Equation: An equation of the form |ax + b| = c

3. Steps for Solving Replace the absolute value symbol | | with ± ( )
2) Separate into two inequalities
a) one with the + ( )
b) one with the – ( )
3) Now solve for BOTH resulting in two answers.
Remember to distribute the negative.

4. Example 1
Solve.

5. Example 2: Pay Close Attention!
Positive negative positive ≠ negative (NOT possible!) No solution

6. Example 3
Solve.
Check.

7. Example 4
Solve.

8. Example 5
Solve.

9. Write an absolute value equation that has 4 and 10 as its solutions.3 3
= 6
Midpoint
= 7
Distance from Endpoint to Midpoint
= 3

10. Write an absolute value equation that has
5 and 19 as its solutions.
Midpoint
Distance from Endpoint to Midpoint =
= 7