1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objective 1.8 Solving Absolute-Value Equations and Inequalities Write, solve, and graph absolute-value equations and inequalities in mathematical and real-world situations.

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Term absolute value 1.8 Solving Absolute-Value Equations and Inequalities

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Absolute Value Let x be any real number. 1.8 Solving Absolute-Value Equations and Inequalities Algebraic definition: If x  0, then  x  = x. If x  0, then  x  =  x. Geometric definition: The absolute value of x is the distance from x to 0 on the number line.

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Absolute-Value Equations If a > 0 and |x| = a, then x = a or x = –a. 1.8 Solving Absolute-Value Equations and Inequalities

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Solve and graph absolute-value equations. 4|x| =8 1.8 Solving Absolute-Value Equations and Inequalities 4x =8or4x =–8 x =2orx =–2

6. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Solve and graph absolute-value equations. |x + 1| =7 1.8 Solving Absolute-Value Equations and Inequalities x + 1 =7orx + 1 =–7 x =6orx =–8

7. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties 1.8 Solving Absolute-Value Equations and Inequalities Absolute-Value Inequalities If a > 0 and |x| –a and x < a. If a > 0 and |x| > a, then x a. Similar statements are true for |x|  a and |x|  a.

8. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Solve and graph absolute-value inequalities. |x + 52|  76 x + 52  76or–(x + 52)  76 x  24orx  – 128 1.8 Solving Absolute-Value Equations and Inequalities

9. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Solve and graph absolute-value inequalities. |x + 52|  76 x + 52  76and–(x + 52)  76 x  24and x  –128 1.8 Solving Absolute-Value Equations and Inequalities TOC