I know that the arithmetic mean of a set of numbers is the sum of the numbers divided by the number of numbers. So, if the arithmetic mean of 7, 2, $x$ and 10 is 9, then I can write an equation like this: $\frac{7+2+x+10}{4}=9$. To solve for $x$, I can multiply both sides of the equation by 4 and simplify: $7+2+x+10=36$. Then, I can subtract 7 and 2 and 10 from both sides and get: $x=36-7-2-10=17$. 
The arithmetic mean of 7, 2, $x$ and 10 is 9. What is the value of $x$?