Answer
$(-∞, -3)$ U $(2, ∞)$
Work Step by Step
$5/(x+3) < 1$
$x+3=0$
$x+3-3=0-3$
$x=-3$
The denominator is zero 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 $x=-4$, $x=0$, $x=3$
$x=-4$
$5/(x+3) < 1$
$5/(-4+3) < 1$
$5/-1 < 1$
$-5 < 1$ (true)
$x=0$
$5/(x+3) < 1$
$5/(0+3) < 1$
$5/3 < 1$ (false)
$x=3$
$5/(x+3) < 1$
$5/(3+3) < 1$
$5/6 < 1$ (true)
$(-∞, -3)$ U $(2, ∞)$
