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Pres   Absolute Value Inequalities (Section 1.8)
Pres   Absolute Value Inequalities (Section 1.8)
Pres   Absolute Value Inequalities (Section 1.8)
Pres   Absolute Value Inequalities (Section 1.8)
Pres   Absolute Value Inequalities (Section 1.8)
Pres   Absolute Value Inequalities (Section 1.8)
Pres   Absolute Value Inequalities (Section 1.8)
Pres   Absolute Value Inequalities (Section 1.8)
Pres   Absolute Value Inequalities (Section 1.8)
Pres   Absolute Value Inequalities (Section 1.8)
Pres   Absolute Value Inequalities (Section 1.8)
Pres   Absolute Value Inequalities (Section 1.8)
Pres   Absolute Value Inequalities (Section 1.8)
Pres   Absolute Value Inequalities (Section 1.8)
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Pres Absolute Value Inequalities (Section 1.8)

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  • 1. Absolute Value
  • 2. Absolute Value
  • 3. Rules and Properties <ul><li>Absolute-Value Equations </li></ul><ul><li>If a > 0 and | x | = a , then x = a or x = – a . </li></ul>1.8 Solving Absolute-Value Equations and Inequalities Absolute-Value Inequalities If a > 0 and | x | < a , then x > – a and x < a . If a > 0 and | x | > a , then x < – a or x > a . Similar statements are true for | x |  a and | x |  a.
  • 4. Absolute Value Rules <ul><li>If you start with an “=“ sign then you will have an “or” statement. </li></ul><ul><li>If you start with a “<“ or a “ ≤” then you will have an “and” statement. </li></ul><ul><li>If you start with a “>” or a “≥” then you will have an “or” statement. </li></ul>
  • 5. Example 1 <ul><li>Solve and graph absolute-value equations. </li></ul>| x + 1| = 7 1.8 Solving Absolute-Value Equations and Inequalities
  • 6. Example 1 <ul><li>Solve and graph absolute-value equations. </li></ul>| x + 1| = 7 1.8 Solving Absolute-Value Equations and Inequalities x + 1 = 7 or x + 1 = –7 x = 6 or x = –8
  • 7. Example 2 <ul><li>Solve and graph absolute-value equations. </li></ul>4| x | = 8 1.8 Solving Absolute-Value Equations and Inequalities
  • 8. Example 2 <ul><li>Solve and graph absolute-value equations. </li></ul>4| x | = 8 1.8 Solving Absolute-Value Equations and Inequalities 4 x = 8 or 4 x = –8 x = 2 or x = –2
  • 9. Example 3 |x - 4| = x + 1
  • 10. Example 3 |x - 4| = x + 1 x = x + 5 or x – 4 = -x - 1 0 = 5 or 2x – 4 = -1 x - 4 = x + 1 x - 4 = -(x + 1) No Solution or 2x = 3 No Solution or x = 3/2 3/2
  • 11. Example 4 <ul><li>Solve and graph absolute-value inequalities. </li></ul>| x + 52|  76 1.8 Solving Absolute-Value Equations and Inequalities
  • 12. Example 4 <ul><li>Solve and graph absolute-value inequalities. </li></ul>| x + 52|  76 x + 52  76 or x + 52  - 76 x  24 or x  – 128 1.8 Solving Absolute-Value Equations and Inequalities
  • 13. Example 5 <ul><li>Solve and graph absolute-value inequalities. </li></ul>| x + 52|  76 1.8 Solving Absolute-Value Equations and Inequalities
  • 14. Example 5 <ul><li>Solve and graph absolute-value inequalities. </li></ul>| x + 52|  76 x + 52  76 and x + 52  -76 x  24 and x  –128 1.8 Solving Absolute-Value Equations and Inequalities

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