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

1 Answer
Jan 18, 2017

Answer:

The answer is #x in [-1, 0 [ #

Explanation:

We cannot cross over.

Let's rewrite the inequality

#(x+3)/x+2<=0#

#(x+3+2x)/(x)<=0#

#(3x+3)/(x)<=0#

#(3(x+1))/x<=0#

Let #f(x)=(3(x+1))/x#

Let's do the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-1##color(white)(aaaaaaa)##0##color(white)(aaaaaa)##+oo#

#color(white)(aaaa)##x+1##color(white)(aaaa)##-##color(white)(aaaaaa)##+##color(white)(aa)##∥##color(white)(aa)##+#

#color(white)(aaaa)##x##color(white)(aaaaaaaa)##-##color(white)(aaaaaa)##-##color(white)(aa)##∥##color(white)(aa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##+##color(white)(aaaaa)##-##color(white)(aa)##∥##color(white)(aa)##+#

Therefore,

#f(x)<=0#, when #x in [-1, 0 [ #