6.4 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 / A1.1.3.1.35-5 Absolute Value InequalitiesVocabularyAbsolute Value distance from zero

Every Absolute Value Inequality has TWO answers. 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 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 1 0 1 2 3 4 5 6 7 8 If | x | > 2, then any number bigger than 2 or less than -2 is a solution of the inequality.OR problemEvery problem has 2 answers!< and problems have AND solutions

> and problems have OR solutionsSolve |x+5|< 6x + 5 can be any number between -6 and 6.

-6 < x + 5 < 6 -5 - 5 -5 -11 < x < 1

-11 < x < 1Solve | x 4 | > 3Positivex 4 > 3 +4 +4 x > 7Negativex 4 < -3 +4 +4 x < 1x 4 can be anything bigger than 3 or smaller than -3.ORx > 7 OR x < 1Examples|x - 7|< 10-3 < x < 17|x 2| 9x 11 OR x -7|5x + 8| 12-4 x 0.8|2x + 1|- 3 > 6x > 8 OR x < -5|2x + 5|+ 1 6-5 x 0

Solve |p + 4| < 6. Then graph the solution set.

A.p < 2B.p > 10C. 10 < p < 2D. 2 < p < 10

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

PracticeWorksheet Tall TalentSpecial ProblemsSolve |p 5| < 2No solution

Solve |5x 1| 2All real numbers

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