1) the "math" in the brackets should be capitol and you need a space after pi so it can register that that's a separate call.

and you need to close it with [\MATH ] (minus the space)

2) I don't know what you mean with the "or" but here goes:

For the last question there is no way for that to be true. Because if you move things around you get |w| = -6 and an absolute value's not going to be negative.

But.. hmm..

(case 1: w > 0 : fails, by above

case 2: )

I'm not sure about what I wrote in there, I think that was from graphing and when you had to find the intervals for which the equation worked or something. I don't know if it still applies but you can take it and show it to someone who knows what they're doing, unlike me obviously. :P