Modeling Real-World Absolute Value Inequalities

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

• T < 15 or T > 25

• 10 < T < 30

• T = 20

• 15 < T < 25

A car's speed must not differ from 60 miles per hour by more than 10 miles per hour. Write an absolute value inequality to model this situation and find the range of acceptable speeds.

• 50 ≤ s ≤ 70

• 30 ≤ s ≤ 90

• 40 ≤ s ≤ 80

• 60 ≤ s ≤ 100

A student scored within 3 points of a perfect score of 100 on a test. Write an absolute value inequality to represent the student's score and determine the possible scores.

• The possible scores are 97, 98, 99, and 100.

• 99, 100, 101, and 102

• 90, 91, 92, and 93

• 95, 96, 97, and 98

The height of a plant is measured to be 15 inches, but it can vary by 2 inches. Write an absolute value inequality to express the height range and find the minimum and maximum heights.

• Minimum height: 12 inches, Maximum height: 18 inches

• Minimum height: 14 inches, Maximum height: 16 inches

• Minimum height: 13 inches, Maximum height: 17 inches

• Minimum height: 10 inches, Maximum height: 20 inches

A basketball player wants to maintain a weight that is within 5 pounds of 180 pounds. Write an absolute value inequality to model this situation and calculate the acceptable weight range.

• 170 ≤ x ≤ 180

• 175 ≤ x ≤ 190

• 175 ≤ x ≤ 185

• 180 ≤ x ≤ 190

A store advertises that a product is priced within $10 of $50. Write an absolute value inequality to represent the price range and determine the minimum and maximum prices.

• Minimum price: 30, Maximum price: 70

• Minimum price: 45, Maximum price: 55

• Minimum price: 35, Maximum price: 65

• Minimum price: 40, Maximum price: 60

A runner's time for a mile is 7 minutes, but it can vary by 15 seconds. Write an absolute value inequality to express the range of possible times and find the fastest and slowest times.

• Fastest time: 6 minutes 30 seconds

• Slowest time: 7 minutes 45 seconds

• Fastest time: 7 minutes 10 seconds

• Fastest time: 6 minutes 45 seconds, Slowest time: 7 minutes 15 seconds

A family wants to keep their monthly expenses within $200 of their budget of $1500. Write an absolute value inequality to model this situation and calculate the range of acceptable expenses.

• 1300 ≤ x ≤ 1700

• 1200 ≤ x ≤ 1600

• 1000 ≤ x ≤ 2000

• 1400 ≤ x ≤ 1800

A student needs to score within 4 points of an average score of 85 on their assignments. Write an absolute value inequality to represent this and find the range of acceptable scores.

• The range of acceptable scores is (80, 90).

• The range of acceptable scores is (75, 95).

• The range of acceptable scores is (81, 89).

• The range of acceptable scores is (82, 88).

A delivery service guarantees that packages will arrive within 3 miles of the destination. Write an absolute value inequality to model this situation and determine the range of acceptable distances from the destination.

• 0 <= x <= 5

• -3 <= x <= 0

• 0 <= x <= 3

• 3 < x <= 6