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Understanding Absolute Value Equations and Inequalities: Key Concepts and Strategies

This lesson covers the fundamental concepts of absolute value equations and inequalities. Students will learn that the absolute value of a number represents its distance from zero on a number line. The lesson emphasizes the importance of checking for extraneous solutions, which are incorrect results derived from solving equations. In addition, it explains how to solve multi-step absolute value equations and handle inequalities based on the sign. Examples are provided to illustrate these concepts, alongside homework assignments to reinforce learning.

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Understanding Absolute Value Equations and Inequalities: Key Concepts and Strategies

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  1. Lesson 1-5 Absolute Value Equations and Inequalities

  2. Vocabulary • The absolute value of a number is its distance from zero on the number line and distance is nonnegative. • An extraneous solution is a solution of an equation derived from an original equation but it is not a solution.

  3. Solving Absolute Value Equations • Check:

  4. Checking for Extraneous Solutions Example: Check:

  5. Solving Multi-Step Absolute Value Equations Example:

  6. Example #1

  7. Example #2

  8. Properties of Absolute Value Inequalities The solution will depend upon the inequality sign.

  9. Example 3 (Solving “greater than” inequalities) • Solve Graph the solution.

  10. Solving “less than” Inequalities

  11. Example #4 (solving “less than” inequalities

  12. Homework: • Pp 36-37, #1-15 odd and 35-43 odd • Thursday - Homework Quiz 1-4 through 1-6

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