Writing & Interpreting Absolute Value Inequalities

A temperature range is considered safe if it is within 5 degrees of 70°F. Write an absolute value inequality to represent this situation.

• |T - 75| ≤ 5

• |T - 70| < 5

• |T + 70| ≤ 5

• |T - 70| ≤ 5

A car's speed must not differ from 60 miles per hour by more than 10 miles per hour. Write the absolute value inequality for this scenario.

• |x - 50| ≤ 10

• |x + 60| ≤ 10

• |x - 60| ≤ 10

• |x - 70| < 10

A student scored 85 on a test and wants to ensure their score is within 3 points of the average score. Write an absolute value inequality to express this.

• |x - 85| ≤ 3

• |x - 80| ≤ 5

• |x + 85| ≤ 3

• |x - 85| < 3

The height of a plant is measured to be 12 inches, but it can vary by 2 inches. Write an absolute value inequality to represent the possible heights of the plant.

• |h - 12| ≤ 2

• |h + 12| ≤ 2

• |h - 10| ≤ 2

• |h - 14| ≤ 2

A basketball player wants to maintain a weight that is within 4 pounds of 180 pounds. Write the absolute value inequality that represents this situation.

• |x - 176| ≥ 4

• |x - 180| ≤ 4

• |x - 200| ≤ 4

• |x + 180| ≤ 4

A store advertises that a product's price is $50, but it can vary by $8. Write an absolute value inequality to express the range of possible prices.

• |x - 50| < 8

• |x - 50| ≥ 8

• |x + 50| ≤ 8

• |x - 50| ≤ 8

A runner's time for a marathon is 4 hours, but they want to finish within 15 minutes of that time. Write an absolute value inequality to represent this.

• |t - 4| < 0.25

• |t + 4| ≤ 0.25

• |t - 4| ≥ 0.25

• |t - 4| ≤ 0.25

A student needs to score within 5 points of 90 on their final exam to pass. Write the absolute value inequality that represents this requirement.

• |x - 85| ≤ 5

• |x - 95| < 5

• |x - 90| ≤ 5

• |x + 90| ≤ 5

A factory's production output is 200 units, but it can fluctuate by 20 units. Write an absolute value inequality to express the acceptable range of production.

• |x - 180| ≤ 20

• |x + 200| ≤ 20

• |x - 200| ≤ 20

• |x - 220| ≤ 20

A hiker wants to stay within 3 miles of a trailhead that is 10 miles away. Write an absolute value inequality to represent the distance the hiker can be from the trailhead.

• |d - 10| < 3

• |d + 10| ≤ 3

• |d - 10| ≤ 3

• |d - 7| ≤ 3