How do you solve #6/x<2# using a sign chart?

1 Answer
Jun 11, 2017

Answer:

The solution is #x in (-oo,0) uu (3,+oo)#

Explanation:

Let's rewrite and simplify the inequality

We cannot do crossing over

#6/x<2#

#6/x-2<0#

#(6-2x)/x<0#

#(2(3-x))/x<0#

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

Let's build the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaaaa)##0##color(white)(aaaaaaa)##3##color(white)(aaaaa)##+oo#

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

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

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

Therefore,

#f(x)<0#, when # x in (-oo,0) uu (3,+oo)# graph{(6/x)-2 [-22.81, 22.8, -11.4, 11.42]}