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

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

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.

Example 1 Solve.

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

Example 3 Solve. Check.

Example 4 Solve.

Example 5 Solve.

Write an absolute value equation that has 4 and 10 as its solutions. 3 3 0 1 2 3 4 5 6 7 8 9 10 10 - 4 = 6 Midpoint = 7 Distance from Endpoint to Midpoint = 3

Write an absolute value equation that has 5 and 19 as its solutions. Midpoint Distance from Endpoint to Midpoint = 12 - 5 = 7