KöMaL 2008 A450

The function $f\colon \mathbb{R}\to \mathbb{R}$ satisfies the equation $f$ ( $x$+$f$($y$) ) +$f$ ( $f$($x$)+$y$ ) =2$x$+2$y$. Prove that $f$(2$x$)=2$f$($x$) for all real numbers $x$.