Answer: The required length of BM is 32 units.
Step-by-step explanation: Given that the point M is the midpoint of the line segment AB where
[tex]AM=2x+8,\\\\BM=3x-4.[/tex]
We are to find the length of BM.
Since the point M is the midpoint of the segment AB, so we must have
[tex]AM=BM\\\\\Rightarrow 2x+8=3x-4\\\\\Rightarrow 3x-2x=8+4\\\\\Rightarrow x=12.[/tex]
Therefore, the length of BM is given by
[tex]BM=3\times12-4=36-4=32.[/tex]
Thus, the required length of BM is 32 units.
