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carcass
If \(y-x > x + y\), where x and y are integers, which of the following must be true?

I. \(x < 0\)
II. \(y > 0 \)
III. \(xy > 0 \)

A. I only
B. II only
C. I and II only
D. I and III only
E. II and III only.
 

Solving this question comes down to just understanding the basics of algebra. 

Given: \(y-x > x + y\)

We can cancel off y from both sides to get: 2x < 0 which is same as x < 0

What does it mean when we say "we can cancel off y from both sides?" It means that it has no impact on the inequality whatsoever. 

Say if we are given x < 0, if I add y to both sides, I get y + x < y (the inequality doesn't change)
If I add 2z on both sides, I get 2z + y + x < 2z + y (the inequality still doesn't change)

Hence y can be anything, it doesn't matter. 
So the only thing  y-x > x + y tells us is that x < 0

Answer (A)
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