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3.8 Solving Equations Involving Absolute Value • Goal: Solve equations involving absolute value. Absolute Value • The distance from “0” on the number line The number inside the Absolute Value Bars may be negative or positive to begin with The number in the Absolute Value Bars always comes out positive Absolute Value Remember: Goals for today: An equation can Solve equations involving absolute value. have more than |x| - 7 = 9one solution x-7=9 +7 +7 x = 16 Is there any other value for “x” that makes the equation true? x = -16 Solve for “y”: |y| = 8 y 8 and y 8 y 8 Absolute Value To solve equations involving absolute value. 1) Solve for |x| using the usual steps. 3|x| - 5 = 10 3IxI =15 IxI = 5 2) Write your solution as the positive number and its opposite. x= -5 and 5 |m| - 7 = 9 +7 +7 |m| = 16 m = ±16 |x| + 4 = 9 -4 -4 |x| = 5 x=5 or x = -5 Solve for y: 2 |y| + 1 = 15 -1 -1 2|y| = 14 2 2 |y| = 7 y = 7 or y = - 7 y 7 Solve for y: |-8| + |y| = |-21| + |2| 8 + |y| = 21 + 2 y = ±15 Solve for y: -3|y| + 4 = -11 3 y 15 3 3 y 5 y 5 Solve for y: (7) | y | 10 (7) 7 y = 70 or y = - 70 Solve for y: 15 y 2 2 y 3 5 2 5 y 3 5 5 2 y 15 2 2 15 y 2 Solve for y: |y| = -7 No Solution Solve for y: -5|y| + 8 = 18 8 8 5 y 10 -5 -5 y 2 No Solution Assignment: page 146 2-30 even 13 – 22 is mental math. Show each step.