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Question 13

If $$x + y < y$$ and $$x - y > x$$, then the most appropriate order relation between $$x$$ and $$y$$ is

Solution

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Cancelling $$y$$ from $$x + y < y$$ gives $$x < 0$$, and cancelling $$x$$ from $$x - y > x$$ gives $$-y > 0$$, that is $$y < 0$$. Nothing more can be said about which of $$x$$ and $$y$$ is larger, so the correct relation is $$x < 0$$ and $$y < 0$$.

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