Mastering Absolute Value Inequalities in Real-Life Scenarios

1. A temperature range is defined as being within 5 degrees of 20 degrees. Write an absolute value inequality to represent this situation and solve it.

• 10 < T < 30

• 20 < T < 35

• 5 < T < 15

• 15 < T < 25

2. The distance from a point on a number line to 3 is at most 7. Write the absolute value inequality and find the possible values.

• [-4, 10]

• [0, 7]

• [-3, 8]

• [-5, 9]

3. A car's speed must not deviate more than 10 miles per hour from the speed limit of 55 mph. Write the absolute value inequality and solve for the range of acceptable speeds.

• 50 ≤ s ≤ 70

• 40 ≤ s ≤ 60

• 45 ≤ s ≤ 65

• 30 ≤ s ≤ 50

4. A student scored 15 points above or below the average score of 80 in a test. Write an absolute value inequality to represent this and find the range of scores.

• The range of scores is from 60 to 100.

• The range of scores is from 65 to 95.

• The range of scores is from 70 to 90.

• The range of scores is from 75 to 85.

5. The height of a plant is measured to be 12 inches, but it can vary by 3 inches. Write the absolute value inequality and determine the possible height range.

• The possible height range is from 6 inches to 12 inches.

• The possible height range is from 10 inches to 14 inches.

• The possible height range is from 8 inches to 16 inches.

• The possible height range is from 9 inches to 15 inches.

6. A runner wants to maintain a pace that is within 2 minutes of their average pace of 8 minutes per mile. Write the absolute value inequality and solve for the acceptable pace range.

• 6 <= p <= 10

• 5 <= p <= 11

• 7 <= p <= 9

• 4 <= p <= 6

7. A store advertises that a product is priced within $5 of $30. Write the absolute value inequality and find the possible price range for the product.

• $20 to $30

• $15 to $25

• $30 to $40

• The possible price range for the product is $25 to $35.

8. The elevation of a mountain is 5000 feet, but it can vary by 200 feet. Write the absolute value inequality and determine the range of elevations.

• The range of elevations is from 4700 feet to 5300 feet.

• The range of elevations is from 4800 feet to 5200 feet.

• The range of elevations is from 4500 feet to 5500 feet.

• The range of elevations is from 4900 feet to 5100 feet.

9. A student needs to score within 4 points of a passing score of 70 on a test. Write the absolute value inequality and find the range of scores that are passing.

• The range of passing scores is from 68 to 72.

• The range of passing scores is from 65 to 75.

• The range of passing scores is from 60 to 80.

• The range of passing scores is from 66 to 74.

10. A bike's tire pressure should be within 3 psi of the recommended pressure of 30 psi. Write the absolute value inequality and solve for the acceptable tire pressure range.

• 25 psi to 35 psi

• 27 psi to 33 psi

• 30 psi to 36 psi

• 20 psi to 40 psi