Ch 6.5 Absolute Value Equations Objective: To solve one variable absolute value equations

Definition Rules Absolute-Value: The distance from the origin (0) Absolute-Value Equation: An equation of the form |ax + b| = c Rules 1. Isolate the absolute value expression 2. Replace the absolute value symbol | | with ± ( ) 3. Separate into two equations or inequalities a) one with the + ( ) b) one with the – ( ) 4. Solve for BOTH resulting in two answers.

Example 1 Example 2 = = − ± (x) = 5 Positive ≠ negative NOT possible! Solve = Solve = − ± (x) = 5 Positive ≠ negative NOT possible! + (x) = 5 - (x) = 5 -1 -1 x = 5 x = -5 No solution

± (x - 3) = 15 Example 3 Solve − = + (x - 3) = 15 - (x - 3) = 15 -1 -1 − = ± (x - 3) = 15 + (x - 3) = 15 - (x - 3) = 15 -1 -1 - = - = - + + + + = = -

± (x - 4) = 6 Example 4 Solve - = - = + (x - 4) = 6 - (x - 4) = 6 - = - = ± (x - 4) = 6 + (x - 4) = 6 - (x - 4) = 6 -1 -1 - = - = - = = -

± (2x - 3) = 25 Example 5 Solve - + = - - - = - (2x - 3) = 25 - + = - - - = ± (2x - 3) = 25 - (2x - 3) = 25 + (2x - 3) = 25 -1 -1 - = - = - + + + + = = − = = −

Classwork 2) Solve |x| = −9 1) Solve |n| = 6

|n| - 4 = 1 4) Solve 3|x| = 9 3) Solve

|p + 7| = 11 6) Solve |-8 + x| = 15 5) Solve

-2|m + 8| = -36 8) Solve 6|n - 7| = 42 7) Solve