If $x+\left|y\right|=2y,$ then $y$ as a function of $x$ is

If $x+\left|y\right|=2y$, then $y$ can be written in terms of x as

$y=\left\{\begin{array}{l}x\hspace{0.25em} \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\text{if y}\ge 0\\ \frac{x}{3}\hspace{0.25em} \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\text{if y}<0\end{array}\right.$

Therefore, y as a function of x is defined for all x and is continuous at x = 0, but it is not differentiable at x = 0, because

         $\underset{h\to 0+}{lim} \frac{f(0+h)-f\left(0\right)}{h}=1$

and   $\underset{h\to 0-}{lim} \frac{f(0+h)-f\left(0\right)}{h}=\frac{1}{3}$