Answer
X=8
AB=36
Work Step by Step
We know a midpoint divides a segment into 2 segments of equal length.
Therefore, AM = MB, so we can set their equations equal to each other.
2(x+1)=3(x-2)
2x+2=3x-6
8=x
So, x is 8.
Next, the question asks us to solve for AB.
Since AM=MB, and AM+MB=AB through the Segment Addition Postulate, 2AM=AB (Or 2 MB=AB, or AM+MB=AB)
Substituting x into the equation for AM gives 2(8+1), or 18
Substituting x into the equation for MB gives 3(8-2), or 18
By addition OR multiplication, depending on how you solve it, AB=36
