1.7: Solve Absolute Value Equations 1/18/2019 Absolute Value Equations Section 1.7 1/18/2019 3:38 AM 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 1

1.7: Solve Absolute Value Equations Definitions Absolute Value is the distance from zero. When graphing in Absolute Value, it is shaped in a “v” >, <, or ≠ requires the dot being OPEN or PARENTHESIS >, <, or = required the dot being CLOSED or BRACKETS Extraneous Solutions are solutions that must be rejected because it does not satisfy the original equation 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations

1.7: Solve Absolute Value Equations 1/18/2019 Quick Examples 1) What is the absolute value of 25? 2) |–25| = x, what is/are x? 3) |x| = 25, what is/are x? 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations

1.7: Solve Absolute Value Equations 1/18/2019 More Quick Examples |π – 3| |3 – π| 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 4

1.7: Solve Absolute Value Equations 1/18/2019 Steps Isolate the absolute value equation Write two equations, with one answer being positive and other is negative Solve each equation Check by plugging each solution and make sure there aren’t any extraneous solutions 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 5

1.7: Solve Absolute Value Equations 1/18/2019 Example 1 Solve |x – 4| = 9 and list any extraneous solutions. 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 6

1.7: Solve Absolute Value Equations 1/18/2019 Example 2 Solve |2x + 12| = 4x and list any extraneous solutions. 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 7

1.7: Solve Absolute Value Equations 1/18/2019 Your Turn Solve |4x – 1| = 2x + 9 and list any extraneous solutions 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 8

1.7: Solve Absolute Value Equations 1/18/2019 Example 3 Solve |2x + 5| – 3 = 8 and list any extraneous solutions 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 9

1.7: Solve Absolute Value Equations 1/18/2019 Example 4 Solve 2|x + 1| = 14 and list any extraneous solutions. 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 10

1.7: Solve Absolute Value Equations 1/18/2019 Your Turn Solve 8|3x – 10| – 12 = 20 and list any extraneous solutions. 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 11

1.7: Solve Absolute Value Equations 1/18/2019 Example 5 Solve |x + 4| = 3x – 8 and list any extraneous solutions. 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 12

1.7: Solve Absolute Value Equations 1/18/2019 Example 6 Solve |3x + 1| = |2x + 3| and list any extraneous solutions. 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 13

1.7: Solve Absolute Value Equations 1/18/2019 Your Turn Solve |x + 1| = |x – 1| and list any extraneous solutions. 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 14

1.7: Solve Absolute Value Equations 1/18/2019 Example 7 Solve |3x – 1|= 0 and list any extraneous solutions. 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 15

1.7: Solve Absolute Value Equations 1/18/2019 Example 8 Solve |5x – 1| = –2 and list any extraneous solutions. 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 16

1.7: Solve Absolute Value Equations 1/18/2019 Example 9 Solve –2|x + 1| = 14 and list any extraneous solutions. 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 17

1.7: Solve Absolute Value Equations 1/18/2019 Your Turn Solve |x + 1| = |x – 1| and list any extraneous solutions. 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 18

1.7: Solve Absolute Value Equations 1/18/2019 Example 10 Solve |x| + |x + 3| = 3 and list any extraneous solutions 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 19

1.7: Solve Absolute Value Equations 1/18/2019 Your Turn Solve |x| + |x – 5| = 5 and list any extraneous solutions. 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 20

1.7: Solve Absolute Value Equations 1/18/2019 Assignment Absolute Value Worksheet A 1/18/2019 3:38 AM 1.7: Solve Absolute Value Equations 21