The mean of the set is the sum of the numbers divided by the number of numbers, which is 3 in this case. So the mean is $\frac{6 + x + 22}{3}$. The median of the set is the middle number, which is $x$. So I have the equation $\frac{6 + x + 22}{3} = x$. I can multiply both sides by 3 to get rid of the fraction: $6 + x + 22 = 3x$. I can subtract $x$ from both sides to isolate the terms with $x$ on one side: $6 + 22 = 2x$. I can simplify the left side by adding 6 and 22: $28 = 2x$. I can divide both sides by 2 to solve for $x$: $x = 14$. 
The mean of the increasing ordered set of numbers, $\{6, x, 22\}$, is equal to the median. What is the value of $x$?