You should have $\displaystyle 10 + 12 = 22$ in the numerator whereas you have 12. The method is fine though
$\displaystyle 22-x = 30$
Remember you can (and should) always check the value of x obtained but subbing it into the original equation and seeing if it works
Here's a useful trick: when solving algebraic equations, you never need to check an answer key, because it's quite easy to check the answer yourself. All you have to do is plug your answer into the original equation, and see if it satisfies the equality. So what do you get when you plug your answer into the original equation?