Answer
$(-∞, 5)$
Work Step by Step
$3/(y-5) < 0$
The denominator is zero when $y=5$.
$3/(y-5) = 0$
$3/(y-5)*(y-5) =0*(y-5)$
$3 = 0$
This is false, so we have two intervals to test.
The two intervals to test are $(-∞, 5)$ and $(5, ∞)$.
We pick $y=0$ and $y=6$ to see where the inequality is true.
$y=0$
$3/(y-5) < 0$
$3/(0-5) < 0$
$3/-5 <0$
$-3/5 < 0$ (true)
$y=6$
$3/(y-5) < 0$
$3/(6-5) < 0$
$3/1 < 0$
$3 < 0$ (false)
The inequality is true over the interval $(-∞, 5)$.
