Absolute Value Inequalities: Real-World Applications for 9th Graders

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

• |x - 15| ≤ 5

• |x - 20| ≤ 5

• |x + 20| ≤ 5

• |x - 25| < 5

A student scored 85 on a test, and the teacher said the scores were within 10 points of the average. Write an inequality to express the range of possible average scores.

• 70 < A < 90

• 75 < A < 95

• 80 < A < 100

• 75 < A < 85

A car's speed must not differ from 60 miles per hour by more than 15 miles per hour. Write an absolute value inequality to represent this speed limit.

• |s - 45| ≤ 15

• |s - 60| ≥ 15

• |s - 60| ≤ 15

• |s + 60| ≤ 15

The height of a plant is measured to be 30 cm, with a tolerance of 4 cm. Write an absolute value inequality to express the acceptable height range of the plant.

• |h - 30| ≤ 4

• |h - 30| < 4

• |h - 25| ≤ 4

• |h + 30| ≤ 4

A basketball player wants to maintain a weight that is within 8 pounds of 180 pounds. Write an absolute value inequality to represent this weight range.

• |w - 180| ≤ 8

• |w + 180| ≤ 8

• |w - 172| ≤ 8

• |w - 190| ≥ 8

A store advertises that a product is priced within $5 of $50. Write an absolute value inequality to represent the possible prices of the product.

• |p - 50| < 5

• |p + 50| ≤ 5

• |p - 50| ≤ 5

• |p - 45| ≤ 5

A runner's time for a race is 25 minutes, and it can vary by 3 minutes. Write an absolute value inequality to express the range of possible race times.

• |t - 25| ≤ 3

• |t - 22| ≤ 5

• |t - 25| < 3

• |t + 25| ≤ 3

A student needs to score within 12 points of 75 on a final exam to pass. Write an absolute value inequality to represent the passing score range.

• |x - 75| ≤ 12

• |x + 75| ≤ 12

• |x - 60| ≤ 12

• |x - 75| < 12

A factory produces items that should weigh 200 grams, with a tolerance of 10 grams. Write an absolute value inequality to express the acceptable weight range of the items.

• |x - 200| ≤ 10

• |x - 200| < 10

• |x - 210| ≤ 10

• |x + 200| ≤ 10

A person is trying to keep their daily calorie intake within 200 calories of 2500 calories. Write an absolute value inequality to represent this calorie range.

• |x + 2500| ≤ 200

• |x - 2400| < 200

• |x - 2500| ≤ 200

• |x - 2500| ≥ 200