Goal: Solve absolute value inequalities. Eligible Content: A / A / A / A Absolute Value Inequalities

Vocabulary Absolute Value – distance from zero Every Absolute Value Inequality has TWO answers.

 8  7  6  5  4  3  2  If | x |  8, then any number between  8 and 8 is a solution of the inequality. AND problem

 8  7  6  5  4  3  2  If | x | > 2, then any number bigger than 2 or less than -2 is a solution of the inequality. OR problem

Every problem has 2 answers! < and ≤ problems have AND solutions > and ≥ problems have OR solutions

Solve |x+5|< 6 x + 5 can be any number between -6 and < x + 5 < < x < 1

Solve | x  4 | > 3 Positive x – 4 > x > 7 Negative x – 4 < x < 1 x – 4 can be anything bigger than 3 or smaller than -3. OR x > 7 OR x < 1

Examples 1. |x - 7|< < x < |x – 2|≥ 9 x ≥ 11 OR x ≤ |5x + 8|≤ ≤ x ≤ |2x + 1|- 3 > 6 x > 8 OR x < |2x + 5|+ 1 ≤ 6 -5 ≤ x ≤ 0

Solve |p + 4| < 6. Then graph the solution set. A.p < 2 B.p > –10 C. –10 < p < 2 D. –2 < p < 10

Solve |2m – 2| > 6. Then graph the solution set. A.m > –2 or m < 4 B.m > –2 or m > 4 C.–2 < m < 4 D.m 4

Practice Worksheet – “Tall Talent”

Special Problems 1. Solve |p – 5| < –2 No solution 2. Solve |5x – 1| ≥ –2 All real numbers

Homework Page 314 #8-18 even Solve and graph each solution! Each problems should have 2 answers!!