Question

A truck is said to get 18 miles per gallon on a highway, but this value can fluctuate, at most, by 4 miles per gallon. Which of the following absolute value inequalities matches this scenario?

a. |x + 18| ≤ 4
b. |x + 18| > 4
c. |x – 4| > 18
d. |x – 18| ≤ 4

Answer 1

The correct absolute value inequality matching the truck's fuel efficiency scenario is |x – 18| ≤ 4, which includes all fuel efficiencies from 14 to 22 miles per gallon.

Step-by-step explanation:

The question requires determining which absolute value inequality describes the scenario where a truck's fuel efficiency on a highway is 18 miles per gallon, with a possible fluctuation of 4 miles per gallon. We want to express an inequality that includes all the values that are within 4 miles per gallon of 18, either higher or lower. The correct inequality for this situation is |x – 18| ≤ 4. This means that the variable x, representing the truck's fuel efficiency, can be within 4 units above or below 18. It encompasses all the possible fuel efficiencies from 14 to 22 miles per gallon.