Answer
(-infinity, $2)$ U $(11/4$, infinity)
Work Step by Step
$3/(x-2) < 4$
Denominator is zero when $x=2$
$3/(x-2) < 4$
$3*(x-2)/(x-2) < 4*(x-2)$
$3 < 4x-8$
$11 < 4x$
$11/4 < 4x/4$
$11/4 < x$
(-infinity, $2)$
$(2, 11/4)$
$(11/4$, infinity)
Let $x=0$, $x=2.5$, $x=4$
$x=0$
$3/(x-2) < 4$
$3/(0-2) < 4$
$3/-2 < 4$
$-3/2 < 4$ (true)
$x=2.5$
$3/(x-2) < 4$
$3/(2.5-2) < 4$
$3/.5 <4$
$6 < 4$ (false)
$x=4$
$3/(x-2) < 4$
$3/(4-2) < 4$
$3/2 < 4$ (true)
