Exploring and Solving Absolute Value Inequalities

1. A temperature range is defined as being within 5 degrees of 20 degrees. Write and solve the absolute value inequality to find the range of temperatures.

• 15 ≤ T ≤ 25

• 20 ≤ T ≤ 22

• 12 ≤ T ≤ 18

• 10 ≤ T ≤ 30

2. A car's speed must not exceed 60 miles per hour, but it can also be 5 miles per hour below that. Write the absolute value inequality and graph it.

• |x + 60| ≤ 5

• |x - 55| ≤ 5

• |x - 50| ≤ 10

• |x - 60| ≤ 5

3. The height of a plant is measured to be 15 cm, but it can vary by 3 cm. Write the absolute value inequality and determine the possible height range.

• The possible height range is 9 cm to 21 cm.

• The possible height range is 10 cm to 20 cm.

• The possible height range is 12 cm to 18 cm.

• The possible height range is 15 cm to 15 cm.

4. A student scored 85 on a test, and the teacher allows a margin of error of 4 points. Write the absolute value inequality and solve for the range of acceptable scores.

• 82 ≤ x ≤ 86

• 80 ≤ x ≤ 88

• 75 ≤ x ≤ 95

• 81 ≤ x ≤ 89

5. A delivery truck must stay within 10 miles of its route, which is 30 miles long. Write the absolute value inequality and graph the solution.

• |x + 15| ≤ 10

• |x - 15| ≤ 10

• |x - 10| ≤ 15

• |x - 20| ≤ 5

6. A basketball player needs to maintain a weight of 180 pounds, with a tolerance of 5 pounds. Write the absolute value inequality and find the acceptable weight range.

• 170 to 180 pounds

• The acceptable weight range is 175 to 185 pounds.

• 180 to 190 pounds

• 175 to 190 pounds

7. A store advertises a discount of $10 on a product, but the price can vary by $2. Write the absolute value inequality and solve for the price range.

• $10 < price < $14

• $18 < price < $22

• $20 < price < $24

• $15 < price < $19

8. A runner's time for a race is 25 minutes, with a possible variation of 3 minutes. Write the absolute value inequality and determine the range of possible times.

• The range of possible times is from 22 minutes to 28 minutes.

• The range of possible times is from 20 minutes to 30 minutes.

• The range of possible times is from 24 minutes to 26 minutes.

• The range of possible times is from 21 minutes to 29 minutes.

9. A family wants to keep their monthly expenses within $200 of their budget of $1500. Write the absolute value inequality and solve for the range of expenses.

• 1200 ≤ x ≤ 1800

• 1300 ≤ x ≤ 1700

• 1000 ≤ x ≤ 2000

• 1400 ≤ x ≤ 1600

10. A student needs to score within 10 points of a passing score of 70 on a test. Write the absolute value inequality and find the range of scores that would be considered passing.

• 80 to 90

• 61 to 79

• 70 to 80

• 50 to 60