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SOLVE ABSOLUTE VALUE INEQUALITIES January 21, 2014 Pages 398-400

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Do you remember??? 1. Solve |x – 6| = 4. 2. Solve |x + 5| – 8 = 2. ANSWER 2, 10 ANSWER –15, 5

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Solve the inequality. Graph your solution. 1.1. – 6 x > The distance between x and 0 is greater than or equal to 6. So, x ≤ – 6 or x ≥ 6. ANSWER The solutions are all real numbers less than or equal to – 6 or greater than or equal to 6. SOLUTION

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2.2. < x 0.5 – The distance between x and 0 is less than or equal to 0.5.So, to – 0.5 ≤ x ≤ 0.5. SOLUTION ANSWER The solutions are all real numbers greater than or equal to – 0.5 and less than or equal to 0.5.

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Solve the inequality. Graph your solution. 3. x 8 < SOLUTION The distance between x and 0 is less equal to 8. So, – 8 ≤ x ≤ 8. ANSWER The solutions are all real numbers greater than or equal to – 8 and less than or equal to 8. –9 –8 –7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 8 9..

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4. u < 3.5 SOLUTION The distance between x and 0 is less or equal to 3.5. So, – 3.5 < u < 3.5. ANSWER The solutions are all real numbers greater than or equal to – 3.5 & less than or equal to 3.5... –4.5 –3.5 –2.5 –1.5 0 1.5 2.5 3.5 4.5.

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SOLUTION The distance between x and 0 is less or greater than so, 2 3 2 3 2 3 v 3 3 – 2 3 3 3 1 3 2 3 – 1 3 – 0 ANSWER The solutions are all real numbers greater than and less than 2 3 – 2 3 5. v > 2 3

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Solve x – 5 ≥ 7. Graph your solution. Write original inequality. x – 5 7 < – x – 5 7 – > or x – 5 7 – > Rewrite as compound inequality. x –2 < – or – >x 12 Add 5 to each side. ANSWER The solutions are all real numbers less than or equal to – 2 or greater than or equal to 12. Check several solutions in the original inequality. 6.

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Solve – 4x – 5 + 3 < 9. Graph your solution. – 4x –5 + 3 < 9 –6 <–4x – 5 < 6 – 4x – 5 < 6 –1 <–4x < 11 0.25 > x > –2.75 –2.75 < x < 0.25 Write original inequality. Subtract 3 from each side. Rewrite as compound inequality. Add 5 to each expression. Rewrite in the form a < x < b. Divide each expression by – 4. Reverse inequality symbol. 7.

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ANSWER The solutions are all real numbers greater than –2.75 and less than 0.25.

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SOLUTION Solve the inequality. x + 3 > 8 8. Write original inequality. Rewrite as compound inequality. Add – 3 to each side. x + 3 > 8 or x + 3 < 8 x + 3 > 8 x < – 11 or x > 5 ANSWER The solutions are all real numbers less than – 11 or greater than to 5.

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SOLUTION 2w – 1 < 11 9. Write original inequality. Rewrite as compound inequality. Add 1 to each side. 2w – 1 < 11 or 2w – 1 > 11 2w – 1 < – 11 w < – 5 or w > 6 Divide by 2 to each side ANSWER – 5 < w <– 6 or 2w < – 10 2w > 12

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SOLUTION Write original inequality. Divide by each side by 3. Rewrite as compound inequality. 10.3 5m – 6 – 8 13 < – < – Add 8 to each side. 3 5m – 6 21< – |5m – 6| 7< – – 7 5m 6 7 < – < – – 1 ≤ 5m ≤ 13 Add 6 to each side. – 0.2 ≤ m ≤ 2.6 Simplify. The solutions are all real numbers greater than or equal to – 0.2 and less than or equal to 2.6.

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HOMEWORK Page 401, #4-20, even

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