1 8 Solving AbsoluteValue Equations and Inequalities Objective

1. 8 Solving Absolute-Value Equations and Inequalities Objective • Write, solve, and graph absolute-value equations and inequalities in mathematical and real-world situations. Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

1. 8 Solving Absolute-Value Equations and Inequalities Glossary Term absolute value Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

1. 8 Solving Absolute-Value Equations and Inequalities Rules and Properties Absolute Value Let x be any real number. Algebraic definition: If x 0, then x = x. Geometric definition: The absolute value of x is the distance from x to 0 on the number line. Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

1. 8 Solving Absolute-Value Equations and Inequalities Rules and Properties Absolute-Value Equations If a > 0 and |x| = a, then x = a or x = –a. Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

1. 8 Solving Absolute-Value Equations and Inequalities Key Skills Solve and graph absolute-value equations. 4|x| = 8 4 x = 8 or 4 x = – 8 x=2 or x = – 2 Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

1. 8 Solving Absolute-Value Equations and Inequalities Key Skills Solve and graph absolute-value equations. |x + 1| = 7 x+1=7 or x + 1 = – 7 x=6 or x = – 8 Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

1. 8 Solving Absolute-Value Equations and Inequalities Rules and Properties Absolute-Value Inequalities If a > 0 and |x| < a, then x > –a and x < a. If a > 0 and |x| > a, then x < –a and x > a. Similar statements are true for |x| a and |x| a. Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

1. 8 Solving Absolute-Value Equations and Inequalities Key Skills Solve and graph absolute-value inequalities. |x + 52| 76 x + 52 76 or x 24 or –(x + 52) 76 x – 128 Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

1. 8 Solving Absolute-Value Equations and Inequalities Key Skills Solve and graph absolute-value inequalities. |x + 52| 76 x + 52 76 and x 24 and –(x + 52) 76 x – 128 TOC Copyright © by Holt, Rinehart and Winston. All Rights Reserved.