Why does the sign flip?

Just think about it logically Zac,  I'll use a simpler example

$$k^2>25$$

 If k=6 then k^2=36 so this makes the statement true

If k=-6 then x^2=36 so this makes the statement true too.

For any value of k between -5 and +5 the statement will be false.

So it will be true when

k>5   and when  k<-5

It may help you understand if you draw a number line.  I often think of number lines when I answer inequalities.

Have I answered your question or were you hoping for something different ?

Thanks, I think I understand. The surds might have been throwing me off. 

Yes whenever there is a complication in a question that gets in the way of grasping the technique needed, always get rid of it and look at an similar example with kinder numbers or letters.

I still do this quite regularly