Mastering Absolute Value Inequalities in Real Life Scenarios

A temperature is recorded as -5 degrees Celsius. If the temperature can vary by at most 3 degrees, what is the range of temperatures? Write an absolute value inequality to represent this situation.

• -5 to -2 degrees

• -3 to 0 degrees

• The range of temperatures is from -8 to -2 degrees.

• -10 to -4 degrees

A student scored 75 on a test. If the teacher allows a margin of error of 10 points, what scores are acceptable? Write an absolute value inequality to express this.

• |x - 75| ≤ 10

• |x - 70| ≤ 5

• |x - 75| < 10

• |x + 75| ≤ 10

A car's speed is measured at 60 miles per hour. If the speed can vary by 5 miles per hour, what is the acceptable speed range? Write an absolute value inequality for this scenario.

• 55 ≤ s ≤ 65

• 50 ≤ s ≤ 60

• 60 ≤ s ≤ 70

• 55 ≤ s ≤ 75

A bank account has a balance of $200. If the balance can fluctuate by $50, what is the range of possible balances? Write an absolute value inequality to represent this situation.

• The range of possible balances is $150 to $250.

• The range of possible balances is $50 to $150.

• The range of possible balances is $200 to $400.

• The range of possible balances is $100 to $300.

A runner's time for a race is 30 minutes. If the time can vary by 2 minutes, what is the acceptable range of times? Write an absolute value inequality to express this.

• |t - 32| ≤ 2

• |t - 28| ≤ 2

• |t + 30| ≤ 2

• |t - 30| ≤ 2

A store's profit is $1500. If the profit can vary by $300, what is the range of possible profits? Write an absolute value inequality to represent this situation.

• The range of possible profits is $[1500, 1800].

• The range of possible profits is $[1200, 1500].

• The range of possible profits is $[1000, 2000].

• The range of possible profits is $[1200, 1800].

A class has an average score of 85. If the average can vary by 4 points, what is the acceptable range of average scores? Write an absolute value inequality for this scenario.

• The acceptable range of average scores is 81 to 89, and the absolute value inequality is |x - 85| ≤ 4.

• The acceptable range of average scores is 75 to 95, and the absolute value inequality is |x - 85| = 4.

• The acceptable range of average scores is 82 to 88, and the absolute value inequality is |x - 85| ≥ 4.

• The acceptable range of average scores is 80 to 90, and the absolute value inequality is |x - 85| < 5.

A plant needs to be watered when the soil moisture level is between 20% and 40%. If the ideal moisture level is 30%, write an absolute value inequality to represent the acceptable moisture levels.

• |x - 30| < 10

• |x + 30| <= 10

• |x - 30| <= 10

• |x - 20| <= 10

A cyclist's distance from home is 10 miles. If the distance can vary by 3 miles, what is the range of distances from home? Write an absolute value inequality to express this.

• 5 ≤ d ≤ 15

• 8 ≤ d ≤ 12

• 6 ≤ d ≤ 14

• 7 ≤ d ≤ 13

A phone's battery life is at 80%. If it can vary by 10%, what is the acceptable range of battery life? Write an absolute value inequality to represent this situation.

• |x - 70| ≤ 10

• |x - 90| ≤ 10

• |x + 80| ≤ 10

• |x - 80| ≤ 10