Solve for x. Please help and please show work, thanks!

Answer: 5
Step-by-step explanation:
We can use ratios / proportions to solve for x. I am going to have the shorter segment on the top of our fractions (the numerator), and the longer segments on the bottom (the denominator).
[tex]\frac{10}{10+12} =\frac{4x-5}{33}[/tex]
[tex]\frac{10}{22} =\frac{4x-5}{33}[/tex]
Now I am going to cross multiply:
10 * 33 = 22(4x - 5)
330 = 88x - 110
440 = 88x
5 = x
x = 5