Answer
$(3, 15)$
Work Step by Step
$4x/(x-3) \geq 5$
Denominator is zero when $x=3$
$4x/(x-3) \geq 5$
$4x/(x-3) = 5$
$4x*(x-3)/(x-3) =5*(x-3)$
$4x = 5x-15$
$4x+15=5x-15+15$
$4x+15=5x$
$4x+15-4x=5x-4x$
$15=x$
(-infinity, $3)$
$(3, 15)$
$(15$, infinity)
Let $x=0$, $x=10$, $x=20$
$x=0$
$4x/(x-3) \geq 5$
$4*0/(0-3) \geq 5$
$0/-3 \geq 5$
$0 \geq 5$ (false)
$x=10$
$4x/(x-3) \geq 5$
$4*10/(10-3) \geq 5$
$40/7 \geq 5$ (true)
$x=20$
$4x/(x-3) \geq 5$
$4*20/(20-3) \geq 5$
$80/17 \geq 5$ (false)
