Solve the following math problem step by step. The last line of your response should be of the form Answer: \boxed{$Answer} where $Answer is the answer to the problem.

<image>In parallelogram $ABCD$, $\overline{BD}$ and $\overline{AC}$ intersect at $E$. If $AE = 9$, $BE = 3x - 7$, and $DE = x + 5$, find $x$.