Good morning all!

I am studying to prepare myself for a PreCalc/Trig class in the Fall and I am stuck on a quadratic compound inequality with no examples to use and no professor to ask. I have attached a copy of the work I have done on this exercise so far. Would any of you guys mind letting me know where I went wrong ?

Questions I had while solving:

When I derived the two possible values for the absolute value, should I have eliminated part of the domain since it has both positive and negative 3? If so, why?

Is there a better way I can analyze the domains I found to make it easier to find the intersections?

Any help would be really appreciated.

Lenora