Mastering Absolute Value Inequalities and Graphs

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

• (15, 25)

• (25, 35)

• (30, 50)

• (20, 40)

A car's speed must not exceed 60 mph, but it can also be 5 mph below that. Write an absolute value inequality to represent this situation and solve for the speed range.

• s < 55 or s > 60

• 60 < s ≤ 65

• 50 ≤ s ≤ 55

• 55 ≤ s ≤ 60

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 height range and find the possible heights.

• The possible heights of the plant are between 10 inches and 14 inches.

• The possible heights of the plant are between 6 inches and 18 inches.

• The possible heights of the plant are between 9 inches and 15 inches inclusive.

• The possible heights of the plant are between 5 inches and 20 inches.

A student scored 85 on a test, and the teacher allows a margin of error of 4 points. Write an absolute value inequality to represent the acceptable score range and solve it.

• 75 ≤ x ≤ 95

• 80 ≤ x ≤ 84

• 81 ≤ x ≤ 89

• 86 ≤ x ≤ 90

A store advertises that a product is priced at $50, but the price can vary by $10. Write an absolute value inequality to represent the price range and find the possible prices.

• The possible prices are between $40 and $60.

• The possible prices are between $30 and $70.

• The possible prices are between $45 and $55.

• The possible prices are between $20 and $80.

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.

• (1, 7)

• (3, 5)

• (2, 6)

• (0, 4)

A runner wants to maintain a pace that is within 2 minutes of 8 minutes per mile. Write an absolute value inequality to represent this situation and find the acceptable pace range.

• 7 <= p <= 11

• 5 <= p <= 9

• 4 <= p <= 12

• 6 <= p <= 10

A basketball player has an average score of 20 points per game, with a variation of 5 points. Write an absolute value inequality to represent the scoring range and solve it.

• 20 ≤ x ≤ 35

• 15 ≤ x ≤ 25

• 15 ≤ x ≤ 20

• 10 ≤ x ≤ 30

A factory produces items that should weigh 10 kg, with a tolerance of 1 kg. Write an absolute value inequality to represent the acceptable weight range and find the possible weights.

• 10 kg ≤ weight ≤ 15 kg

• 7 kg ≤ weight ≤ 13 kg

• 9 kg ≤ weight ≤ 11 kg

• 8 kg ≤ weight ≤ 12 kg

A student needs to score within 10 points of a passing score of 75 on a test. Write an absolute value inequality to represent the acceptable score range and solve it.

• 65 ≤ x ≤ 90

• 60 ≤ x ≤ 70

• 75 < x < 85

• 65 ≤ x ≤ 85