How to determine whether expression is positive or negative?

Question

Given expressions $|x - 3 + y|$ and $|x + 3 + y|$ how can I determine, whether are those positive or negative, and determine their value in the intervals of:

1. $y < -x - 3$
2. $y \in [-x - 3, 3 - x)$
3. $y > 3 - x$

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Edit: I forget to add, that there are two another conditons $x \geq 3$ and $y < 0$.