Math Problem Statement

solve

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

Solution

We are given two points, EE and FF, on a number line, with the following information:

  • The distance between EE and FF is 5 units, i.e., EF=5EF = 5.
  • FF is located at 13-13.

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

Solution:

The distance between EE and FF is 5, which means that EE could be either 5 units to the left or 5 units to the right of FF.

This gives two possible equations:

  1. E=F5E = F - 5
  2. E=F+5E = F + 5

Since F=13F = -13, we substitute that into both equations:

  1. E=135=18E = -13 - 5 = -18
  2. E=13+5=8E = -13 + 5 = -8

Thus, the two possible locations of EE are 18-18 and 8-8.

Final answer:

The possible locations of EE are E=18E = -18 and E=8E = -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 FF 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.

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Math Problem Analysis

Mathematical Concepts

Number Line
Distance on a Number Line

Formulas

E = F - Distance
E = F + Distance

Theorems

Concept of distance between points on a number line

Suitable Grade Level

Grades 6-8