5.6 HW – Solve Absolute Value Inequalitiesmrsgriggsclassroom.weebly.com/uploads/8/5/8/0/... ·...
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5.6 HW – Solve Absolute Value Inequalities Determine whether the given value is a solution of the inequality. 1. 4| x – 5| +6 < 14; 10
2. 3| x + 2| –2 > 7; x = –3
3. –| x – 4| + 8 > 1; x = 10 4. –|3 – 2x| + 4 > 0; x = –1
Solve the inequality then graph your solution – you do not have to number every dash. 5. | x | ≤ 5
6. | x + 1| > 2
7. | x –3| ≤ 5
8. | x + 5| ≥1
9. | 2x + 3| ≤4
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Match the inequality with the description.
10. The distance between x and 2 is less than or equal to 4. 1. | x – 4| ≤ 2
11. The distance between x and 4 is less than or equal to 2 2. | x – 2| ≤ 4
12. The distance between x and 4 is greater than or equal to 4 3. | x – 2| ≥ 2
13. The distance between x and 2 is greater than or equal to 2 4. | x – 4| ≥ 4
Write the verbal sentence as an inequality and then solve the inequality. 14. The distance between x and 3 is
greater than 5. 15. The distance between x and 22 is less
than 7. 16. The distance between x and 4 is less
than or equal to 2.
17. The distance between x and 26 is greater than or equal to 1.
18. The distance between x and 27 is less
than 2.
19. Body Temperature An adult’s body temperature is considered to be normal if it is 98.6°F
with an absolute deviation of 1°F. a. Write an absolute value inequality that represents the normal temperature range.
b. Solve the inequality. What is the temperature range?
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20. Car Mileage Your car averages 32 miles per gallon on the highway. The actual mileage varies from the average by 5 miles per gallon. a. Write an absolute value inequality that represents the mileage range of your car.
b. Solve the inequality. What is the mileage range?