posted by Jim .
Is it possible for AB = 10, BC = 2x + 5 and AC = 5x, given that point B is the midpoint
No. I answered the same question last week.
The total length of 10 would have to be equal to 7x + 5. That means
7x = 5
x = 5/7
You have an additional requirement that
2x + 5 = 5x, since B is the midpoint.
3x = 5; x = 5/3
These two requirements cannot both be satisfied.