To solve absolute value equations and inequalities in one variable Ch 2.4 Absolute Value Objective: To solve absolute value equations and inequalities in one variable

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 - = -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 - = - = - = = = =

Example 6 Example 7 ± (x) < 5 ± (x) > 5 + (x) < 5 Solve and graph Solve and graph ± (x) < 5 ± (x) > 5 + (x) < 5 - (x) < 5 + (x) > 5 - (x) > 5 -1 -1 -1 -1 x < 5 x > -5 x > 5 x < -5 -5 0 5 -5 0 5

x > 9 |n| < 6 Classwork 2) Solve and graph. 1) Solve and graph. -6 6 -9 9

|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