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If $x>|y|>z$, compare quantity A with quantity B (i.e. quantity A is greater, less or equal to quantity B, or it can't be determined from the given information)

Quantity A: $x+y$

Quantity B: $|y| +z$

I solved it by plugin values in the equation. For example, if x=2, y= 1 and z=0 then quantity A> quantity B. But if x=3, y=-2 and z=0 then quantity B> quantity A. So, we cannot determine about these two quantities from the given information. But I think, there is a smarter way than this. As this equation is a compound inequality a lot of things can happen, I guess. But, I am not getting the total picture of it without plug in method. Can anyone clarify?

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You seem to have spotted that $y \ge 0 \implies A \gt B$ as in your first example

Meanwhile if $y \lt 0$ then $2y = z-x \iff A=B$ and $2y \gt z-x \iff A \gt B$

Your second example has $y \lt 0$ and $2y \lt z-x $ and thus $A \lt B$

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    $\begingroup$ You could probably say in general that the order of $A$ and $B$ are the same as the order of $2y$ and $(z-x)$ $\endgroup$
    – Henry
    Commented Aug 31, 2016 at 12:40

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