Question

Nickolas is setting up water stations for a 10-mile run. He already has the first one set up 8 miles from the starting line. He needs to set up 2 more that are 1.5 miles on either side of the first water station. The absolute value that models this equation is?

a) ∣x−8∣=1.5
b) ∣x−8∣=3
c) ∣x−8∣=0.5
d) ∣x−8∣=2

Answer 1

The correct absolute value equation that models the positions of the water stations is |x - 8| = 1.5. It represents the two additional water stations that are 1.5 miles on either side of the first station, which is 8 miles from the starting line.

Step-by-step explanation:

Nickolas is planning water stations for a long-distance run and the question involves determining the absolute value equation that represents the locations of two additional water stations relative to the first one. Given the first station is 8 miles from the starting line, and the other two need to be 1.5 miles on either side of it, we can model the situation with an absolute value equation. We use an absolute value equation because we are considering distances from a point in both directions (1.5 miles to the left and 1.5 miles to the right of the first station).

The correct model is the equation |x - 8| = 1.5. This equation is true for two values of x: one that is 1.5 miles less than 8 (which would be 6.5 miles from the starting line) and one that is 1.5 miles more than 8 (which would be 9.5 miles from the starting line).