what is the value of x?

These are similar triangles so
9/(9+12) = x/ (x+14)
using cross products
9*(x+14) = x*(9+12)
9x+126 = 21x
subtract 9x from each side
126 = 12x
x=10.5
Set up a proportion.
[tex]\frac{x}{14 + x} = \frac{9}{9 + 12}[/tex]
Now cross multiply.
[tex]x(9 + 12) = 9(14 + x)[/tex]
---> [tex]21x = 9x + 126[/tex]
Isolate variable x ----> [tex]21x - 9x = 126[/tex]
----->[tex]12x = 126[/tex]
Once again isolate variable x:
[tex]\frac{12x}{12} = \frac{126}{12}[/tex]
x = 21/2 or 10.5.