Ch 6.6 Absolute Value Inequalities Objective: To solve and graph one variable absolute value inequalities

Rules 1. Isolate the absolute value expression 2. Replace the absolute value symbol | | with ± ( ) 3. Separate into two inequalities a) one with the + ( ) b) one with the – ( ) 4.Solve for BOTH resulting in two answers. Remember: Follow the rules for dividing by a negative “flip” the inequality symbol When graphing, the variable must be on the left side to use the arrowhead

Example 1Example 2 Solve and graph ± (x) < 5 + (x) < 5- (x) < 5 x < 5 x > Solve and graph ± (x) > 5 + (x) > 5- (x) > 5 x > 5 x <

Example 3 Solve and graph: ± (x + 1) > 5 + (x + 1) > 5 - (x + 1) > 5 x > 4 x < |x + 1| > 5 x + 1 > 5 x + 1 < -5 −1

Example 4 Solve and graph: ± (x − 2) < 6 + (x − 2) < 6 - (x − 2) < 6 x < 8 x > − |x − 2| < 6 x − 2 < 6 x − 2 > -6 +2

Example 5 Solve and graph: ± (x − 2) < 3 + (x − 2) < 3 - (x − 2) < 3 x < 5 x > − |x − 2| > -9 x − 2 < 3 x − 2 >

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

3) Solve 4) Solve |n - 4| < 1 |x + 5| > 7

5) Solve 6) Solve |p + 7| - 2 < 9 |-8 + x| + 2 > 6

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