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

1 Answer
Jan 18, 2017

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)xcolor(white)(aaaa)-oocolor(white)(aaaa)-1color(white)(aaaaaaa)0color(white)(aaaaaa)+oo

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

color(white)(aaaa)xcolor(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 [