How do you solve #(3x+6)/(2x-12)<=0# using a sign chart?

1 Answer
Nov 3, 2017

Answer:

The solution is #x in [-2,6)#

Explanation:

Let #f(x)=(3x+6)/(2x-12)=(3(x+2))/(2(x-6))#

Let's build the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaaaa)##-2##color(white)(aaaaaaa)##6##color(white)(aaaaaa)##+oo#

#color(white)(aaaa)##x+2##color(white)(aaaaaa)##-##color(white)(aaa)##0##color(white)(aaa)##+##color(white)(aaaaaa)##+#

#color(white)(aaaa)##x-6##color(white)(aaaaaa)##-##color(white)(aaa)##0##color(white)(aaa)##-##color(white)(aa)##||##color(white)(aaa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaaa)##+##color(white)(aaa)##0##color(white)(aaa)##-##color(white)(aa)##||##color(white)(aaa)##+#

Therefore,

#f(x)<=0# when #x in [-2,6)#

graph{(3x+6)/(2x-12) [-22.8, 22.83, -11.4, 11.4]}