5-5 Absolute Value Inequalities Goal: Solve absolute value inequalities. Eligible Content: A1.1.1.3.1 / A1.1.3.1.1 / A1.1.3.1.2 / A1.1.3.1.3

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

If | x |  8, then any number between 8 and 8 is a solution of the inequality.  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8 AND problem

If | x | > 2, then any number bigger than 2 or less than -2 is a solution of the inequality.  8  7  6  5  4  3  2  1 0 1 2 3 4 5 6 7 8 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 6. -6 < x + 5 < 6 -5 - 5 -5 -11 < x < 1 -11 < x < 1

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

Examples |x - 7|< 10 |x – 2|≥ 9 |5x + 8|≤ 12 |2x + 1| > 9 x ≥ 11 OR x ≤ -7 |5x + 8|≤ 12 -4 ≤ x ≤ 0.8 |2x + 1| > 9 x > 4 OR x < -5 |2x + 5|+ 1 ≤ 6 -5 ≤ x ≤ 0

Solve |p + 4| < 6. Then graph the solution set. 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 < –2 or m > 4

Practice Worksheet – “Tall Talent”

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

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