Answer
(-infinity, $-8)$ U $(-4$, infinity)
Work Step by Step
$x/(x+4)\leq2$
Denominator is zero when $x=-4$
$x/(x+4)\leq2$
$x/(x+4)=2$
$x*(x+4)/(x+4)=2*(x+4)$
$x=2x+8$
$x-8=2x+8-8$
$x-8=2x$
$x-8-x=2x-x$
$-8=x$
(-infinity, $-8)$
$(-8, -4)$
$(-4$, infinity)
Let $x=-10$, $x=-6$, $x=0$
$x=-10$
$x/(x+4)\leq2$
$-10/(-10+4)\leq2$
$-10/-6 \leq 2$
$5/3 \leq 2$ (true)
$x=-6$
$x/(x+4)\leq2$
$-6/(-6+4)\leq2$
$-6/-2 \leq 2$
$3 \leq 2$ (false)
$x=0$
$x/(x+4)\leq2$
$0/(0+4)\leq2$
$0/4 \leq 2$
$0 \leq 2$ (true)
