Question

Find all real numbers x such that x^2 -8>0. Write your final answer in interval notation.

I really just need a starter step. I remember these questions, but I'm not sure how to start. Please help!

Answer 1

x^2 - 8 > 0
x^2 > 8

That should help.

Answer 2

So the sign is flipped because we moved a negative number, right?

Answer 3

no, you can add and subtract anything without flipping the direction. Only if you multiply or divide by a negative value does the direction change.

It's really just a shortcut to moving things to the other side:

-2x < 8
0 < 8+2x
-8 < 2x
-4 < x

That's the same as dividing and flipping at once:

-2x < 8
x > -4