If b is the midpoint of ac, which of the following choices is the value of x?

If B is the midpoint of AC, that means that the distances from A to B and B to C are the same. The distance from A to B is 8x + 4, and the distance from B to C is 10x - 6, so we can set these two equivalent:

8x + 4 = 10x - 6

Solving for x:

4 = 2x - 6 (subtract 8x from both sides)
10 = 2x (add 6 to both sides)
5 = x (divide both sides by 2)

So, x = 5, which is the second option given.