1.8 Solving Absolute-Value Equations and Inequalities Objective Write, solve, and graph absolute-value equations and inequalities in mathematical and real-world situations.

Glossary Term absolute value 1.8 Solving Absolute-Value Equations and Inequalities Glossary Term absolute value

Rules and Properties Absolute Value Let x be any real number. 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. If x  0, thenx= x. Geometric definition: The absolute value of x is the distance from x to 0 on the number line.

Rules and Properties Absolute-Value Equations 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. 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.

Key Skills Solve and graph absolute-value equations. |x + 1| = 7 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

Key Skills Solve and graph absolute-value equations. 4|x| = 8 1.8 Solving Absolute-Value Equations and Inequalities Key Skills Solve and graph absolute-value equations. 4|x| = 8 4x = 8 or 4x = –8 x = 2 or x = –2

Key Skills Solve and graph absolute-value inequalities. |x + 52|  76 1.8 Solving Absolute-Value Equations and Inequalities Key Skills Solve and graph absolute-value inequalities. |x + 52|  76 x + 52  76 or –(x + 52)  76 x  24 or x  –128

Key Skills Solve and graph absolute-value inequalities. |x + 52|  76 1.8 Solving Absolute-Value Equations and Inequalities Key Skills Solve and graph absolute-value inequalities. |x + 52|  76 x + 52  76 and –(x + 52)  76 x  24 and x  –128 TOC