How do you solve $(-2x+5)/(x+6)> -2$ using a sign chart?

Question

1482 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-14T18:13:18

The solution is $x in (-6,+oo)$

We cannot do crossing over, let's do some simplifications

$(-2x+5)/(x+6)>-2$

$(5-2x)/(x+6)+2>0$

$(5-2x+2x+12)/(x+6)>0$

$17/(x+6)>0$

Let $f(x)=17/(x+6)$

Let 's build the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-6$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $x+6$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaa)$ $+$

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

Therefore,

$f(x)>0$ when $x in (-6,+oo)$

graph{17/(x+6) [-32.46, 32.48, -16.24, 16.25]}

How do you solve (-2x+5)/(x+6)> -2(-2x+5)/(x+6)> -2 using a sign chart?