S.O.S. Mathematics CyberBoard

I have some trouble with inequalities, absolute value and show things. Could someone please explain me how it works by solving these:

a)|x|>|x+3|
b) |x-2|/|3x+1| <= 1

And this one:
Let a>=0 Decide for which values of b, the following statements are true:
1)||a|-|b||=|a-b| 2) ||a|-|b||<|a-b|

I know I must separate in different cases, but it isn't so clear to me..
I have a bunch of these to do, I did a few but I want to learn the process by learning of these examples and then apply it to the rest of my homework.

Thanks!

The first one says the distance to 0 is greater than the distance to -3, so draw the line halfway between those points, and color the right half-plane
the second one assume x is not equal to -1/3, then multiply by |3x+1| and you have the same situation, the distance from x to 2 is less than or equal to the distance from 3x to -1.

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Thanks for your help!!!