TeX source:
f(x)=-\left\vert x-13 \right\vert +\dfrac{x}{2} =\left\{\begin{array}{rllll}-(x-13)+\dfrac{x}{2} &=& -\dfrac{1}{2}x+13 & \text{ für } & x\geq13 \cr-\left(-(x-13)\right)+\dfrac{x}{2} &=& \dfrac{3}{2}x-13 & \text{ für } & x < 13\end{array} \right.