Question

Solve for the variable given the following information then find the lengths of AM and AB

Answer 1

Since M is the midpoint (middle) of the line AB, then AM is equal to MB.

3x + 4 = 10x - 17

Collecting like terms

4 + 17 = 10x - 3x

21 = 7x

or

7x = 21

x = 21/7

x = 3

The length AM = 3x + 4 = 3(3) + 4 = 9 + 4 = 13

The length MB = 10x - 17 = 10(3) - 17 = 30 - 17 = 13

The length AB = AM + MB = 13 + 13 = 26

M = (AM + MB) / 2

M = (13 + 13) / 2

M = 26/2

m = 13 units