what is the value of x? explain your answer

For this question, we can use proportional reasoning to find out the answer.
Let us call the point at the other end of line and in between the two expressions, D.
Side AB:AC = BD:DC (remember that ratios are the same as division so you can do the exact same thing with division statements instead).
Now substitute: 8:12 = (x+4):(2x+1).
Now solve (if using division instead of ratios, solve regularily for x):
8:12 = (x+4):(2x+1),
8(2x+1) = 12(x+4),
16x+8 = 12x+48,
16x-12x = 48-8,
4x = 40,
x = 10.

Therefore x = 10