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

Question

$\begin{array}{1 1}(a)\;\text{defined for all real x}\\(b)\;\text{continuous at x=1}\\(c)\;\text{differentiable for all x}\\(d)\;\text{Such that }\large\frac{dy}{dx}=\frac{1}{2} \normalsize\text{for x < 0}\end{array}$