Mastering Absolute Value Inequalities: From Words to Equations

A store sells a shirt for $20. If the price can vary by at most $5, what is the range of prices for the shirt? Translate this into an absolute value inequality and find the solution set.

• $20 to $22

• $15 to $25

• $5 to $15

• $10 to $30

A temperature must stay within 3 degrees of 70°F for a special experiment. Write an absolute value inequality to represent this situation and determine the range of acceptable temperatures.

• 60 ≤ T ≤ 80

• 70 ≤ T ≤ 73

• 65 ≤ T ≤ 75

• 67 ≤ T ≤ 73

A car's speed must not exceed 60 mph, but it can also be 5 mph slower than that. Write an absolute value inequality to express this and find the solution set for the car's speed.

• s < 55

• 55 <= s <= 60

• 50 <= s <= 55

• s > 60

A student needs to score within 10 points of a passing score of 75 on a test. Create an absolute value inequality to represent this and find the range of scores that would be considered passing.

• 60 < x < 70

• 65 < x < 85

• 75 < x < 85

• 65 < x < 80

A basketball player wants to maintain a weight that is within 8 pounds of 180 pounds. Write an absolute value inequality for this situation and determine the acceptable weight range.

• 172 ≤ x ≤ 188

• 180 ≤ x ≤ 200

• 160 ≤ x ≤ 180

• 170 ≤ x ≤ 190

A delivery truck must keep its load weight within 15 pounds of the maximum limit of 200 pounds. Formulate an absolute value inequality and find the solution set for the load weight.

• 200 ≤ x ≤ 230

• 185 ≤ x ≤ 215

• 180 ≤ x ≤ 200

• 175 ≤ x ≤ 195

A hiker wants to stay within 4 miles of a starting point of 12 miles. Write an absolute value inequality to represent this and find the range of distances the hiker can travel.

• 6 ≤ x ≤ 14

• 0 ≤ x ≤ 12

• 10 ≤ x ≤ 18

• 8 ≤ x ≤ 16

A student is practicing for a math test and wants to score within 5 points of their goal of 90 points. Write an absolute value inequality for this scenario and find the possible scores.

• 85 < x < 90

• 85 < x < 95

• 90 < x < 95

• 80 < x < 100

A factory's production must not deviate more than 12 units from a target of 150 units. Create an absolute value inequality to express this and find the range of acceptable production levels.

• 145 ≤ x ≤ 155

• 130 ≤ x ≤ 170

• 140 ≤ x ≤ 160

• 138 ≤ x ≤ 162

A runner wants to maintain a pace that is within 2 minutes of their target pace of 8 minutes per mile. Write an absolute value inequality for this situation and determine the range of paces that are acceptable.

• 7 <= p <= 9

• 6 <= p <= 10

• 4 <= p <= 12

• 5 <= p <= 11