Question

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

Answer 1

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

Explanation:

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]}