Question

How do you solve this inequality?
|x²+2x|>2

Answer 1

consider that \(|x^2+2x|>2\) is the same thing as saying either \(x^2+2x>2\) or \(x^2+2x<-2\) (if you don't believe me convince yourself)

Answer 2

... which means we have two quadratic inequalities:$$x^2+2x-2>0\\x^2+2x+2<0$$do you know how to solve these?

Answer 3

same way you'd any other absolute value inequality as far as I know

the only difference is that is a quadratic function, thus you'd end up with 2 pairs of values for "x"

Answer 4

I think the main problem I'm having is the fact that both of those don't factor normally, so would I just use the quadratic formula?

Answer 5

Pretty much.

Answer 6

Alright, thanks!

Answer 7

yes @OddlyWeird; also note that both are parabolas that open UPWARD, hence if they cross the x-axis they'll look like this: