Answer
$(-∞, -3)$ U $(2, ∞)$
Work Step by Step
$5/ (x+3) <1$
Denominator is zero when $x+3=0$ (or when $x=-3$)
$5/(x+3)=1$
$5/(x+3)*(x+3)=1*(x+3)$
$5=x+3$
$5-3=x+3-3$
$2=x$
Three regions to test: $(-∞, -3)$, $(-3,2)$, $(2, ∞)$
Let $x=-5$, $x=0$, $x=5$
$x=-5$
$5/(x+3) <1$
$5/(-5+3) <1$
$5/-2 <1$
$-5/2 <1$ (true)
$x=0$
$5/(x+3)<1$
$5/(0+3) <1$
$5/3 <1$ (false)
$x=5$
$5/(x+3) <1$
$5/(5+3) <1$
$5/8 <1$ (true)
Thus, the solution set is $(-∞, -3)$ U $(2, ∞)$
