How do you solve $(x+2)/x<=0$ using a sign chart?

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Answer 1 · 2017-02-26T06:51:56

The answer is $x in [-2,0[$

Let $f(x)=(x+2)/x$

The domain of $f(x)$ is $D_f(x)=RR-{0}$

We can build the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-2$ $color(white)(aaaaaaa)$ $0$ $color(white)(aaaaa)$ $+oo$

$color(white)(aaaa)$ $x+2$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaa)$ $+$ $color(white)(aaa)$ $||$ $color(white)(aa)$ $+$

$color(white)(aaaa)$ $x$ $color(white)(aaaaaaaaa)$ $-$ $color(white)(aaaaa)$ $-$ $color(white)(aa)$ $||$ $color(white)(aa)$ $+$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaaa)$ $+$ $color(white)(aaaaa)$ $-$ $color(white)(aaa)$ $||$ $color(white)(aa)$ $+$

Therefore

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

How do you solve (x+2)/x<=0(x+2)/x<=0 using a sign chart?