Catherine: also, I have completely forgotten how to set up and solve a simple inequality involving absolute value
Allison: You need to think about what it means.
The absolute value of any number equal to or greater than 0 is itself. x-->x
The abs value of any number less than 0 is the number*-1, or the number with its sign dropped: x --> -x.
So break down the inequality you see into other inequalities.
|x| - 2 > 3
|x| > 5:
allowable positive values of x satisfy
x > 5
allowable negative values of x satisfy
-x > 5
you "solve" this by switching sides (do you know why you're allowed to do that?)
and that becomes
x < -5
Now, you do |x - 3| < 5 in a similar way. To make yourself less confused, write (x-3) = y
and work on
|y| < 5
Then after you've got that into equations without the abs value, sub back in the x-3.