Question

Your car averages 28 miles per gallon in the city. The actual mileage varies from the average by at most 4 miles per gallon. Write an absolute-value inequality that shows the range for the mileage your car gets.

Short answer

The absolute-value inequality that shows the range for the mileage your car gets is \(|-m + 28| \leq 4\). This indicates that the car's mileage per gallon in the city can be anywhere between 24 and 32 miles.

Step-by-step solution

Understand the Information Given

The car averages 28 miles per gallon of fuel in the city. However, the actual mileage can vary from this average by at most 4 miles, either more or less.

Formulate the Inequality

The inequality must represent the possible range of mileage. In this case, the difference between the actual mileage \(m\) and the average mileage \(28\) is at most \(4\). This can be written as: \(|-m + 28| \leq 4\)

Interpret the Solution

The absolute value inequality \(|-m + 28| \leq 4\) expresses the possible variations from the average mileage. It means that the actual mileage per gallon the car gets in the city is somewhere between 24 and 32 miles.