Question

Solve y>1/2|x|-4 and show work

Answer 1

$y>\frac{1}{2}|x|-4$

$\implies \frac{1}{2}|x|<y+4$

$\implies |x|<2(y+4)$

$\implies-2(y+4)<x<2(y+4)$

The shaded portion is the required answer.

(Please note that it is an open region towards positive y-axis.)