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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