Answer
The solution set is the region shaded GRAY
.
Work Step by Step
We will graph two lines and shade the solution region for each inequality.
1 (red)
$y=2x+4 \quad $dashed line ( sign is $< )$,
y-intercept: $y=4$, point: ($0,4)$
second point:$ x=2, $
$y=-2(2)+4=0$, point: ($2,0)$
Testing (0,0):$\quad 0 < 2(0)+4 \quad ?$
Yes, shade the region containing (0,0)
2 (blue)
$y=x-4 \quad $dashed line ( sign is $< )$,
y-intercept: $y=-4$, point: ($0,-4)$
second point:$ x=4, $
$y=4-4=0$, point: $(4,0)$
Testing (0,0):$\quad 0<0-4 \quad ?$
No, shade the region not containing (0,0)
The solution set is the region with BOTH shadings
The solution set is the region shaded GRAY