Modeling Absolute Value: Real-World Inequalities for 8th Grade

A temperature is recorded as -5 degrees Celsius. If the temperature rises by x degrees, what absolute value equation represents the new temperature being 3 degrees Celsius?

• |x| = 3

• |x| = 8

• |x| = 10

• |x| = 5

A car is traveling at a speed of 60 km/h. If the speed limit is 50 km/h, what absolute value inequality can be used to express how much the car exceeds the speed limit?

• |x + 50| > 10

• |x - 50| < 10

• |x - 60| > 0

• |x - 50| > 10

The distance from a point on a number line to 4 is represented by |x - 4|. If this distance is less than or equal to 3, what inequality represents the possible values of x?

• 1 ≤ x ≤ 7

• x > 7

• x < 1

• -3 < x < 4

A student scored 10 points below the average in a math test. If the average score is represented by a variable a, write an absolute value equation to express the student's score.

• x = a + 10

• x = a - 5

• x = a + 5

• x = a - 10

A store has a sale where the price of an item can vary by no more than $5 from its original price of $20. Write an absolute value inequality to represent the possible sale prices of the item.

• |x - 15| ≤ 5

• |x + 20| ≤ 5

• |x - 20| ≤ 5

• |x - 25| ≤ 5

The height of a plant is measured to be 15 cm. If the height can vary by 2 cm, write an absolute value equation that models the possible heights of the plant.

• |h - 15| ≤ 2

• |h - 15| = 2

• |h + 15| ≤ 2

• |h - 13| ≤ 2

A runner's time for a race is 30 minutes. If the runner's time can vary by 4 minutes, what absolute value inequality represents the range of possible times for the runner?

• |t - 30| ≤ 4

• |t + 30| ≤ 4

• |t - 34| ≤ 4

• |t - 26| < 4

A bank account has a balance of $200. If the balance can fluctuate by $50, write an absolute value equation to represent the possible balances in the account.

• |x + 200| ≤ 50

• |x - 200| ≤ 50

• |x - 150| ≤ 50

• |x - 200| ≥ 50

A delivery truck must stay within 10 miles of a designated route. If the route is represented by the variable r, write an absolute value inequality to express the truck's allowable distance from the route.

• |r| >= 10

• |r| = 10

• |r| <= 10

• |r| < 10

A student needs to score at least 75% on a test to pass. If the test has 40 questions, write an absolute value inequality to determine the minimum number of questions the student must answer correctly.

• 35

• 25

• 40

• 30