How do you solve $(-x-3)/(x+2)<=0$ ?

Question

2025 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-03T17:26:38

The answer is $x in] -oo,-3 ] uu] -2, oo[$

Let $f(x)=(-x-3)/(x+2)$

As we cannot divide by $0$ , the domain of $f(x)$ is $D_f(x)=RR-{-2}$

To solve the inequalty, we do a sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-3$ $color(white)(aaaa)$ $-2$ $color(white)(aaaa)$ $+oo$

$color(white)(aaa)$ $-x-3$ $color(white)(aaaaa)$ $+$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $-$

$color(white)(aaaaa)$ $x+2$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $+$

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

So,

$f(x<=0)$ when

$x in] -oo,-3 ] uu] -2, oo[$

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