How do you solve #(3x+2)/(x-4)<0#?

1 Answer
Jun 6, 2017

Answer:

The solution is #x in (-2/3,4)#

Explanation:

Let #f(x)=(3x+2)/(x-4)#

We build a sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-2/3##color(white)(aaaaaaa)##4##color(white)(aaaaaaaa)##+oo#

#color(white)(aaaa)##3x+2##color(white)(aaaaa)##-##color(white)(aaaaa)##+##color(white)(aaa)##||##color(white)(aaaa)##+#

#color(white)(aaaa)##x-4##color(white)(aaaaaa)##-##color(white)(aaaaa)##-##color(white)(aaa)##||##color(white)(aaaa)##+#

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

Therefore,

#f(x)<0#, when #x in (-2/3,4)#

graph{(3x+2)/(x-4) [-28.86, 28.85, -14.43, 14.45]}