4-6: Absolute Value Equations and Inequalities Essential Question: When do you use “and” and when do you use “or” in an absolute value inequality.

4-6: Absolute Value Equations and Inequalities To solve an absolute value equation: 1.Isolate the absolute value portion of an equation on one side. 2.Write two equations 1.One without the absolute value signs 2.One without the absolute value signs AND flip the signs of every term that wasn’t inside the absolute value signs

4-6: Absolute Value Equations and Inequalities Example 1: Solving an Absolute Value Equation ◦ |x| + 5 = 11Absolute value alone? No ◦ Subtract 5 from both sides ◦ |x| = 6Absolute value alone? Yes ◦ Make Two Equations ◦ x = 6orx = -6

4-6: Absolute Value Equations and Inequalities Your Turn ◦S◦S olve the following ◦|◦| t| - 2 = -1 tt = 1 or t = -1 ◦3◦3 |n| = 15 nn = 5 or n = -5 ◦4◦4 = 3|w| - 2 ww = 2 or w = -2

Example 2: Solving an Absolute Value Equation ◦ |2p + 5| = 11Absolute value alone? Yes ◦ Make Two Equations ◦ 2p + 5 = 11or2p + 5 = -11 ◦ ◦ 2p = 62p = -16 ◦ ÷2 ÷2 ÷2 ÷2 p = 3p = -8

4-6: Absolute Value Equations and Inequalities Your Turn ◦S◦S olve the following ◦|◦| c – 2| = 6 cc = -4 or c = 8 ◦-◦- 5.5 = |t + 2| NNo solution ◦|◦| 7d| = 14 dd = 2 or d = -2

Like absolute value equations, we isolate the absolute value portion and make two equations. In addition to flipping all the signs in the second equation, we also flip the inequality. If the absolute value is on the left: ◦ > and > problems are “or” problems ◦ < and < problems are “and” problems

4-6: Absolute Value Equations and Inequalities Example 3: Solving an Absolute Value Inequality ◦ |v – 3| > 11Absolute value alone? Yes ◦ Make Two Equations ◦ v – 3 > 11or v – 3 < -11 ◦ ◦ v > 14v <

4-6: Absolute Value Equations and Inequalities Your Turn ◦S◦S olve the following. Graph your solution. ◦|◦| w + 2| > 5 ww > 3 or w < -7

Assignment ◦ Worksheet 4-6 ◦ 1 – 27, odd problems