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Solving Absolute Value Equations

Learn how to solve absolute value equations by isolating the equation, writing two equations, solving each equation, and checking for extraneous solutions.

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Solving Absolute Value Equations

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  1. Absolute Value Equations Section 1.7 7/17/2012 1:00 AM 1.7: Solve Absolute Value Equations 1

  2. 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 1.7: Solve Absolute Value Equations

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

  4. More Quick Examples • |π – 3| • |3 – π| 1.7: Solve Absolute Value Equations 4

  5. 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 1.7: Solve Absolute Value Equations 5

  6. Example 1 Solve |x – 4| = 9 and list any extraneous solutions. 1.7: Solve Absolute Value Equations 6

  7. Example 2 Solve |2x + 12| = 4x and list any extraneous solutions. 1.7: Solve Absolute Value Equations 7

  8. Your Turn Solve |4x – 1| = 2x + 9 and list any extraneous solutions 1.7: Solve Absolute Value Equations 8

  9. Example 3 Solve |2x + 5| – 3 = 8 and list any extraneous solutions 1.7: Solve Absolute Value Equations 9

  10. Example 4 Solve 2|x + 1| = 14 and list any extraneous solutions. 1.7: Solve Absolute Value Equations 10

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

  12. Example 5 Solve |x + 4| = 3x – 8 and list any extraneous solutions. 1.7: Solve Absolute Value Equations 12

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

  14. Your Turn Solve |x + 1| = |x – 1| and list any extraneous solutions. 1.7: Solve Absolute Value Equations 14

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

  16. Example 8 Solve |5x – 1| = –2 and list any extraneous solutions. 1.7: Solve Absolute Value Equations 16

  17. Example 9 Solve –2|x + 1| = 14 and list any extraneous solutions. 1.7: Solve Absolute Value Equations 17

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

  19. Example 10 Solve |x| + |x + 3| = 3 and list any extraneous solutions 1.7: Solve Absolute Value Equations 19

  20. Your Turn Solve |x| + |x – 5| = 5 and list any extraneous solutions. 1.7: Solve Absolute Value Equations 20

  21. Assignment Absolute Value Worksheet A 1.7: Solve Absolute Value Equations 21

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