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# Absolute Value Inequalities

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### Absolute Value Inequalities

1. 1. Absolute Value Inequalities
2. 2. Rules: <ul><li>Solve like an absolute value equality. </li></ul><ul><li>BUT in the 2 nd equation, flip the inequality sign too </li></ul>
3. 3. Graphing: <ul><li>After you isolate the absolute value, you can tell what the graph will look like. </li></ul><ul><li>I x I > # -- OR Graph </li></ul><ul><li>I x I < # -- AND Graph </li></ul>
4. 4. I x+4 I > 2 <ul><li>x+4 > 2 </li></ul><ul><li>x+4 < -2 </li></ul><ul><li>-4 -4 </li></ul><ul><li>x > -2 </li></ul><ul><li>-4 -4 </li></ul><ul><li>x < -6 </li></ul>-6 0 -2
5. 5. I d I > 2 <ul><li>d > 2 </li></ul><ul><li>d < -2 </li></ul>2 0 -2
6. 6. I s+5 I < 3 <ul><li>s+5 < 3 </li></ul><ul><li>s+5 > -3 </li></ul><ul><li>-5 -5 </li></ul><ul><li>s < -2 </li></ul><ul><li>-5 -5 </li></ul><ul><li>s > -8 </li></ul>-8 0 -2
7. 7. 3I s+5 I < 3 -6 0 -4
8. 8. I s+5 I - 12 < 3 -20 10
9. 9. I 3.8z I > 17.1 <ul><li>3.8z > 17.1 </li></ul><ul><li>3.8z < -17.1 </li></ul><ul><li>3.8 3.8 </li></ul><ul><li>z > 4.5 </li></ul><ul><li>3.8 3.8 </li></ul><ul><li>z < -4.5 </li></ul>-4.5 0 4.5
10. 10. I 4y+11 I < 7 <ul><li>4y+11 < 7 </li></ul><ul><li>4y+11 > -7 </li></ul><ul><li>-11 -11 </li></ul><ul><li>4y < -4 </li></ul><ul><li>4 4 </li></ul><ul><li>y < -1 </li></ul><ul><li>-11 -11 </li></ul><ul><li>4y > -18 </li></ul><ul><li>4 4 </li></ul><ul><li>y > -4.5 </li></ul>
11. 11. I 4y+11 I < 7 <ul><li>y < -1 </li></ul><ul><li>y > -4.5 </li></ul>-4.5 0 -1