Solving Absolute Value Inequalities in Real-Life Contexts

1. A temperature range is given as |x - 30| < 5. What is the range of temperatures that are considered acceptable?

• (20, 40)

• (30, 45)

• (25, 35)

• (15, 25)

2. The distance from a point on a number line to 4 is less than 3. Write the absolute value inequality and solve for x.

• (0, 4)

• (2, 6)

• (1, 7)

• (3, 5)

3. A car's speed must not deviate more than 10 mph from the speed limit of 55 mph. Write an absolute value inequality to represent this situation and solve it.

• 45 ≤ x ≤ 65

• 45 ≤ x ≤ 70

• 40 ≤ x ≤ 50

• 50 ≤ x ≤ 60

4. The height of a plant is measured to be 12 cm, but it can vary by 2 cm. Write an absolute value inequality to represent the height range and solve it.

• 8 ≤ h ≤ 16

• 10 ≤ h ≤ 12

• 10 ≤ h ≤ 14

• 12 ≤ h ≤ 14

5. A student scored 85 on a test, and the teacher allows a margin of error of 5 points. Write the absolute value inequality and find the range of scores that are acceptable.

• 75 ≤ x ≤ 85

• 85 ≤ x ≤ 95

• 80 ≤ x ≤ 90

• 80 ≤ x ≤ 100

6. The absolute value of a number is greater than 7. Write the inequality and solve for the possible values of the number.

• -7 < x < 7

• x > 7 or x < -7

• x < 7

• x = 7

7. A delivery truck must stay within 15 miles of its starting point. Write an absolute value inequality to represent this and solve for the possible distances from the starting point.

• -10 ≤ x ≤ 10

• x < -15

• -15 ≤ x ≤ 15

• x > 15

8. The temperature in a freezer is set to -10 degrees Celsius, but it can fluctuate by 3 degrees. Write the absolute value inequality and find the range of temperatures.

• The range of temperatures is from -13 degrees Celsius to -7 degrees Celsius.

• The range of temperatures is from -15 degrees Celsius to -5 degrees Celsius.

• The range of temperatures is from -10 degrees Celsius to -3 degrees Celsius.

• The range of temperatures is from -6 degrees Celsius to -4 degrees Celsius.

9. A runner's pace is 8 minutes per mile, but it can vary by 1 minute. Write the absolute value inequality and determine the range of paces.

• 8 to 10 minutes per mile

• 6 to 8 minutes per mile

• 7 to 9 minutes per mile

• 5 to 7 minutes per mile

10. A store advertises that a product is priced at $50, but it can be on sale for up to $5 more or less. Write the absolute value inequality and find the price range for the product.

• $40 to $60

• $45 to $50

• The price range for the product is $45 to $55.

• $48 to $52