Combining inequalities into one inequality Let's say we are given $a$, $b$, $d$ with $1 \leq a, b, d \leq 1000$ and inequalities $x \geq a$, $y \geq b$, and $a+b < x + y \leq a+b+d$.
I need to combine all this and the following into one inequality. Is there a common factor that we can multiply to one or the other or something? Can we exploit the fact that ranges are known? How do we proceed in such a case? Any help is appreciated.

The range defined for one set of value(s) is independent from the range of some other. For instance, $a+b<x+y$ can hold regardless of whether $x\ge a$ or  $y \ge b$ is true. So, there is no way to combine them all into one expression using merely relational operators. 
