Answer
If $x$ is then for any $x\le 0$, then if $y$ is then for any $y\le 0$.
Work Step by Step
When it comes to equality, then the following would be a part of the conclusion:
$$\begin{matrix}
y+\left | y \right |=x+\left | x \right |
\end{matrix}$$
When it comes to their respectable piecewise functions, then the following:
$$\left\{\begin{matrix}
2y & &y>0\\
0 & & y\le 0
\end{matrix}\right.=\left\{\begin{matrix}
2x & &x>0\\
0 & & x\le 0
\end{matrix}\right.$$, which can be graphed as the following you see down below.
Thanks to both $y>0$ and $x>0$, then the folowing would be the general equality:
$$\begin{matrix}
2y=2x\\\\
\frac{2y}{2}=\frac{2x}{2}\\\\
(1)y=(1)x\\
y=x
\end{matrix}$$ with the line visible on the graph as well to show the equality.
Therefore, if $x$ is then for any $x\le 0$, then if $y$ is then for any $y\le 0$.
