Question

Nicolas 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 two more that are 1.5 miles on either side of the first water station. Where will he put the two additional water stations?

A number line divided into increments of 1 and labeled 0 through 10. The number 8 is labeled with Nicolas.

The absolute value equation that models this situation is |x –
|=
.

The two additional water stations will be
and
miles from the starting line.

Nicolas
0 1 2 3 4 5 6 7 8 9 10

Summary
The image depicts a number line ranging from 0 to 10. There is a vertical orange marker at the number 8 with the name “Nicolas” displayed above it.

Answer 1

To determine the locations of the two additional water stations, we start with the first water station, which is located 8 miles from the starting line.

We know that the two additional water stations need to be placed 1.5 miles on either side of the first station at 8 miles.

1. **Calculate the position of the first additional water station:**
- Going 1.5 miles left (towards the starting line):
\[
8 - 1.5 = 6.5 \text{ miles}
\]

2. **Calculate the position of the second additional water station:**
- Going 1.5 miles right (away from the starting line):
\[
8 + 1.5 = 9.5 \text{ miles}
\]

So, the two additional water stations will be located at **6.5 miles** and **9.5 miles** from the starting line.

### Summary
1. **The absolute value equation that models this situation is:**
\[
|x - 8| = 1.5
\]

2. **The two additional water stations will be**
- **6.5 miles** and **9.5 miles** from the starting line.