Doing a line segment finding the midpoint

Question

 

   2x+5            3x+1

._________.___________.

A              M                  B

 

 

This is my probelem im helping my daughter and neither one of us know how to find what x is ive looked everywhere online to try to get how to figure this out and cant find something i understand please help.

Answer 1

    __

If  AB is a line segment, and M is the midpoint, that means that the distance from A to M is equal to the distance from M to B.

This problem merely gives two ways to represent this distance.  Since they are equal, let's find x:

    2x + 5 = 3x + 1

           5 = x + 1         (subtract 2x from both sides)

           4 = x               (subtract 1 from both sides)

 

You could also use 4 to check the answer and determine that each half is 13; the distance from A to B is 26.