AMC 12 2000 Problem 14

When the mean, median, and mode of the list

$$10,2,5,2,4,2,x$$

are arranged in increasing order, they form a non-constant arithmetic progression. What is the sum of all possible real values of $x$?

$\textbf {(A)}\ 3 \textbf {(B)}\ 6 \textbf{(C)}\ 9 \textbf {(D)}\ 17 \textbf {(E)}\ 20$