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# Unit 4.6

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### Unit 4.6

1. 1. Unit 4.6Solve Absolute Value Inequalities Before you solved absolute equations. Now you will solve absolute value inequalities.
2. 2. Example: Using a Number LineRecall that |x| = 3 means that thedistance between x and 0 is 3. 3 –3–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 The solutions to the inequality equation |x| = 3 are 3 and –3.
3. 3. Example: Absolute Value InequalitiesThe inequality |x| < 3 means that thedistance between x and 0 is less than 3.Let’s use the word between to describethe value inequalities. -3 < x < 3 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 Graph of |x| < 3
4. 4. Example: Absolute Value InequalitiesThe inequality |x| > 3 means that thedistance between x and 0 is greater than 3.Let’s use the word beyond to describe thevalue inequalities. x < -3 or x > 3 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 Graph of |x| > 3
5. 5. Example:Solve the Inequality |x| ≥ 6 and graph yoursolution. The distance between x and 0 is greater than or equal 6. So, x ≤ -6 or x ≥ 6. Let’s use the word beyond to describe the value inequalities. –9 –6 –3 0 3 6 Graph of |x| ≥ 6
6. 6. Example:Solve the Inequality |x| ≤ 0.5 and graphyour solution. The distance between x and 0 is less than or equal to 0.5. So, -0.5 ≤ x ≤ 0.5. Let’s use the word between to describe the value inequalities. –1 –0.5 0 0.5 Graph of |x| ≤ 0.5
7. 7. Practice:Solve the Inequality. Graph the Solution. 1. |x| ≤ 8 Groups 1, 2, 3 2. |u| < 3.5 Groups 4, 5 3. |v| > ⅛ Groups 6, 7
8. 8. Practice:Solve the Inequality. Graph the Solution. 1. |x| ≤ 8 Groups 1, 2, 3 2. |u| < 3.5 Groups 4, 5, 6 3. |v| > ⅛ Groups 7, 8, 9
9. 9. Start on your homework for tonight:Textbook Page 229, # 3 - 8