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Understanding Absolute Value Equations and Solutions

Learn how to solve absolute value equations step by step, with examples and practice problems for better understanding. Absolute value represents distance from zero, ensuring positive values. Take advantage of helpful tips to identify and eliminate extraneous solutions efficiently.

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Understanding Absolute Value Equations and Solutions

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  1. Absolute Value Equations Chapter 1.6 1

  2. Absolute Value Equations • Absolute value is the distance from zero. • When graphed into a graphing calculator, it is shaped in a “v” • Using absolute value makes values positive. 2

  3. Quick Examples • Example 1: What is the absolute value of 25? • Example 2:|–25| = x, what is the value of x? • Example 3:|x| = 25, what is the value of x? |25|= 25 25 25 -25 3

  4. Steps for Absolute Value Equations • Write two equations, with one answer being positive and the other being negative • Solve each equation • Check each solution and make sure there aren’t any extraneous solutions 4

  5. Example 1 Solve and check for extraneous solutions 5

  6. Example 2 Solve and check for extraneous solutions 6

  7. Your Turn Solve and check for extraneous solutions 7

  8. Example 3 Solve and check for extraneous solutions 8

  9. Example 4 Solve and check for extraneous solutions 9

  10. Example 5 Solve and check for extraneous solutions 10

  11. Example 6 Solve and check for extraneous solutions 11

  12. Assignment First Half of Worksheet Remember: p. 123 DUE TODAY p. 133 DUE MONDAY 12

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