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Chapter 1.6

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

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Chapter 1.6

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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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