Problems Section: Problems 1161 - 1170

Q1161 Find all values of $x$ (real number) satisfying
\begin{align*}
\frac{x-1}{2004} & + \frac{x-3}{2002} + \frac{x-5}{2000} + \cdots +
\frac{x-2003}{2}\\
= \frac{x-2}{2003} & + \frac{x-4}{2001} + \frac{x-6}{1999} + \cdots +
\frac{x-2004}{1}
\end{align*}