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We are given two points, \(E\) and \(F\), on a number line, with the following information:

- The distance between \(E\) and \(F\) is 5 units, i.e., \(EF = 5\).
- \(F\) is located at \(-13\).

We need to find the possible location(s) of \(E\).

### Solution:

The distance between \(E\) and \(F\) is 5, which means that \(E\) could be either 5 units to the left or 5 units to the right of \(F\). 

This gives two possible equations:
1. \( E = F - 5 \)
2. \( E = F + 5 \)

Since \( F = -13 \), we substitute that into both equations:
1. \( E = -13 - 5 = -18 \)
2. \( E = -13 + 5 = -8 \)

Thus, the two possible locations of \(E\) are \(-18\) and \(-8\).

### Final answer:
The possible locations of \(E\) are \(E = -18\) and \(E = -8\).

Would you like any further details or clarifications?

### Related Questions:
1. What happens if the distance between two points on a number line is given as a variable instead of a number?
2. How would this problem change if point \(F\) was given as a positive number?
3. Can you derive a general formula to find the location of one point given the distance from another point?
4. How do you interpret negative distances in real-world scenarios involving a number line?
5. How can this problem be visualized geometrically?

### Tip:
Always consider both directions when given a distance on a number line to account for all possible locations of the second point.

Suppose that E and F are points on the number line. If EF = 5 and F lies at -13, where could E be located?

Learn how to determine the possible locations of point E given the distance from point F on a number line. This problem focuses on understanding distances and positions on a number line, suitable for students in Grades 6-8.

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