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Solving and Graphing Absolute Value Inequalities: Understanding AND/OR Conditions

This lesson focuses on solving and graphing absolute value inequalities, emphasizing the distinction between "AND" and "OR" conditions, represented by the acronym LAMO (Less And More Or). Students will learn the steps for solving these inequalities, checking for extraneous solutions, and graphing their findings accurately on a number line. Through examples and practice problems, learners will enhance their skills in working with absolute value equations and understand their application in different scenarios.

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Solving and Graphing Absolute Value Inequalities: Understanding AND/OR Conditions

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  1. Finishing from Friday Solve and check for extraneous solutions Hint: Remember the Negative 1

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

  3. ABSOLUTE VALUE INEQUALITIES • Inequalities involve signs that are greater, less, and/or equal to signs. 9/23/2014 2:15 AM 3

  4. 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 4 1-6: Absolute Value Equations

  5. And versus Or… When Solving for Inequalities, remember: Less ThAND GreatOR Than Less Than, “AND” Greater Than, “OR” 5 2-8: Absolute Value Inequalities

  6. Steps for Solving and Graphing Absolute Value Inequalities Identify whether it is an AND/OR inequality (think LAMO) 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 6 1-6: Absolute Value Equations

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

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

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

  10. Example 3 Solve and graph. 2-8: Absolute Value Inequalities

  11. YOUR TURN Solve and graph. 2-8: Absolute Value Inequalities

  12. Example 4 Solve and graph the solution No Solution 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 12 1-6: Absolute Value Equations

  13. Example 5 Solve and graph the solution All Real Numbers 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 13 1-6: Absolute Value Equations

  14. Assignment • Finish WKST from Friday 9/23/2014 2:15 AM 2.9: Absolute Value Inequalities 14 1-6: Absolute Value Equations

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