Mastering Absolute Value Inequalities in Real-Life Scenarios

A store sells a jacket for $80. If the price can vary by at most $10, write an absolute value inequality to represent the possible prices of the jacket. Solve the inequality to find the range of prices.

• 80 ≤ x ≤ 95

• 75 ≤ x ≤ 85

• 60 ≤ x ≤ 100

• 70 ≤ x ≤ 90

The temperature in a city is currently 15 degrees Celsius. If the temperature can fluctuate by no more than 5 degrees, express this situation as an absolute value inequality and determine the possible temperature range.

• The possible temperature range is from 5 degrees Celsius to 15 degrees Celsius.

• The possible temperature range is from 0 degrees Celsius to 10 degrees Celsius.

• The possible temperature range is from 10 degrees Celsius to 20 degrees Celsius.

• The possible temperature range is from 15 degrees Celsius to 25 degrees Celsius.

A car's speed is measured at 60 km/h. If the speedometer can be off by 8 km/h, create an absolute value inequality to represent the possible actual speeds of the car. Solve the inequality to find the range of speeds.

• 54 ≤ x ≤ 62

• 52 ≤ x ≤ 68

• 50 ≤ x ≤ 70

• 60 ≤ x ≤ 64

A student scored 75 on a test. If the score is within 10 points of the average, write an absolute value inequality to represent the average score. Solve the inequality to find the range of possible average scores.

• 60 ≤ x ≤ 75

• 50 ≤ x ≤ 70

• 65 ≤ x ≤ 85

• 80 ≤ x ≤ 90

A bank account has a balance of $500. If the balance can change by at most $50 due to fees or deposits, express this as an absolute value inequality and find the range of possible balances.

• The range of possible balances is between $300 and $700.

• The range of possible balances is between $450 and $500.

• The range of possible balances is between $400 and $600.

• The range of possible balances is between $450 and $550.

A runner's time for a race is 25 minutes. If the time can vary by 3 minutes due to conditions, write an absolute value inequality to represent the possible times. Solve the inequality to find the range of possible race times.

• 21 ≤ t ≤ 27

• 26 ≤ t ≤ 30

• 22 ≤ t ≤ 28

• 20 ≤ t ≤ 24

A factory produces items with a weight of 2 kg. If the weight can vary by 0.5 kg, create an absolute value inequality to represent the acceptable weight range. Solve the inequality to find the minimum and maximum weights.

• Minimum weight: 1 kg, Maximum weight: 2 kg

• Minimum weight: 1.5 kg, Maximum weight: 2.5 kg

• Minimum weight: 2 kg, Maximum weight: 3 kg

• Minimum weight: 1 kg, Maximum weight: 3 kg

A student needs to score within 5 points of a passing grade of 70 on a test. Write an absolute value inequality to represent the scores that would be considered passing. Solve the inequality to find the range of passing scores.

• 70 ≤ x ≤ 80

• 65 ≤ x ≤ 85

• 60 ≤ x ≤ 70

• 65 ≤ x ≤ 75

A phone plan costs $40 per month, but it can vary by $5 due to taxes and fees. Write an absolute value inequality to represent the possible monthly costs. Solve the inequality to find the range of costs.

• 25 ≤ x ≤ 35

• 40 ≤ x ≤ 50

• 35 ≤ x ≤ 45

• 30 ≤ x ≤ 40

A basketball player has an average of 20 points per game. If the player can vary their score by 4 points in any game, express this as an absolute value inequality and determine the range of possible scores for a game.

• The range of possible scores is 16 to 24 points.

• The range of possible scores is 18 to 22 points.

• The range of possible scores is 12 to 28 points.

• The range of possible scores is 10 to 30 points.