Mastering Absolute Value Inequalities in Real Life

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

• (25, 35)

• (15, 25)

• (20, 40)

• (30, 50)

A car's speed must be within 10 miles per hour of the speed limit of 55 mph. Write the absolute value inequality and find the range of acceptable speeds.

• The range of acceptable speeds is 30 mph to 80 mph.

• The range of acceptable speeds is 50 mph to 60 mph.

• The range of acceptable speeds is 40 mph to 70 mph.

• The range of acceptable speeds is 45 mph to 65 mph.

The height of a plant is measured to be 12 inches, but it can vary by 3 inches. Write an absolute value inequality to represent the possible heights of the plant.

• |h - 12| ≤ 3

• |h + 12| ≤ 3

• |h - 15| ≤ 3

• |h - 12| < 3

A student scored 85 on a test, and the teacher allows a margin of error of 4 points. Write an absolute value inequality to find the range of scores that are considered acceptable.

• 80 ≤ x ≤ 88

• 81 ≤ x ≤ 89

• 82 ≤ x ≤ 86

• 75 ≤ x ≤ 95

A store advertises that a product is priced at $50, but the price can vary by $8. Write an absolute value inequality to represent the possible prices of the product.

• |x - 50| ≥ 8

• |x - 50| < 8

• |x - 50| ≤ 8

• |x + 50| ≤ 8

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

• (0, 4)

• (2, 6)

• (3, 5)

• (1, 7)

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 find the range of acceptable paces.

• 7 ≤ p ≤ 11

• 4 ≤ p ≤ 12

• 5 ≤ p ≤ 9

• 6 ≤ p ≤ 10

A family is planning a road trip and wants to stay within 100 miles of their home, which is located at 200 miles. Write the absolute value inequality and determine the range of distances they can travel.

• The range of distances they can travel is from 200 miles to 400 miles.

• The range of distances they can travel is from 150 miles to 250 miles.

• The range of distances they can travel is from 0 miles to 100 miles.

• The range of distances they can travel is from 100 miles to 300 miles.

A student needs to score within 5 points of a passing score of 70 on a math test. Write the absolute value inequality and find the range of scores that would be passing.

• 66 to 74

• 60 to 80

• 70 to 80

• 65 to 75

A dog owner wants to keep their dog within 15 feet of their house. Write the absolute value inequality to represent the distance the dog can roam from the house.

• |x| < 15

• |x| ≥ 15

• |x| = 15

• |x| ≤ 15