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Understanding Absolute Value Inequalities: Key Concepts and Solutions

This chapter explores the fundamentals of absolute value inequalities, starting with the concept of absolute value as the distance from zero. It delves into solving inequalities that involve the terms "greater than," "less than," and "equal to." The guide introduces the LAMO method to remember the distinction between "AND" and "OR" inequalities, presents step-by-step instructions for solving and graphing these inequalities, and includes multiple examples and practice problems for a comprehensive understanding of the topic.

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Understanding Absolute Value Inequalities: Key Concepts and Solutions

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  1. Chapter 1.6 Absolute Value Inequalities 9/23/2014 2:15 AM 1

  2. Absolute Value Inequalities • Absolute value is the distance from zero. • Inequalities involve signs that are greater, less, and/or equal to signs. 9/23/2014 2:15 AM 2

  3. Solving for Absolute Value Inequalities When Solving for Inequalities, remember: Less Than AND More Than OR LAMO 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 3 1-6: Absolute Value Equations

  4. And versus Or… When Solving for Inequalities, remember: Less ThAND GreatOR Than Less Than, “AND” Greater Than, “OR” 4 2-8: Absolute Value Inequalities

  5. Steps for Solving and Graphing Absolute Value Inequalities • Identify whether it is an AND/OR inequality (think LAMO) • ANDwill involve the opposite answer attached to the original equation and carry over the sign • ORwill involve two separate equations with one with the opposite answer and flip the sign • Solve each inequality • Check each solution and make sure there aren’t any extraneous solutions • Graph appropriately on number line 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 5 1-6: Absolute Value Equations

  6. Example 1 Solve and graph the solution | 2 | 0 | –8 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 6 1-6: Absolute Value Equations

  7. Example 2 Solve and graph the solution | 2 | 0 | –9/2 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 7 1-6: Absolute Value Equations

  8. Your Turn Solve and graph the solution | -1/2 | 0 | –7/2 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 8 1-6: Absolute Value Equations

  9. Example 3 Solve and graph the solution 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 9 1-6: Absolute Value Equations

  10. Example 4 Solve and graph the solution 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 10 1-6: Absolute Value Equations

  11. Example 5 Solve 2-8: Absolute Value Inequalities

  12. Example 6 Solve 2-8: Absolute Value Inequalities

  13. Your Turn Solve 2-8: Absolute Value Inequalities

  14. Example 7 Solve and graph the solution No Solution 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 14 1-6: Absolute Value Equations

  15. Example 8 Solve and graph the solution All Real Numbers 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 15 1-6: Absolute Value Equations

  16. Your Turn Solve and graph the solution All Real Numbers 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 16 1-6: Absolute Value Equations

  17. Example 9 Solve 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 17 1-6: Absolute Value Equations

  18. Example 1 Solve and check for extraneous solutions 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 18 1-6: Absolute Value Equations

  19. Example 10 Solve and check for extraneous solutions 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 19 1-6: Absolute Value Equations

  20. Assignment • Pg 154 14, 15, 17-41 odds, 45, 47 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 20 1-6: Absolute Value Equations

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