Question

Write each of the following expressions without using absolute value. |z−7|−|z−9|, if z<7

Answer 1

Here is one way.

$\left\{ \begin{array}{rcl}-2&\mbox{for}&z < 7\\2(z-8)&\mbox{for}&7\le z\le9\\2&\mbox{for}&9 < z\end{array}\right\,$