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# Inequality

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Inequality [#permalink]  24 Mar 2013, 11:00
How would you solve different scenarios for this inequality algebraically (not with number substitution):

Is X-Y positive if X+Y is positive?
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Re: Inequality [#permalink]  24 Mar 2013, 11:16
1
KUDOS
score780 wrote:
How would you solve different scenarios for this inequality algebraically (not with number substitution):

Is X-Y positive if X+Y is positive?

Fact : X+Y is positive
$$x+y>0$$, $$x>-y$$

Question: is X-Y positive?
$$x-y>0$$ , $$x>y$$ ?

You have to try to "lock" one of the terms, your question is too general...

For example if $$y<0$$, $$-y>0$$, we can merge $$x>-y$$ and $$-y>0$$ into $$x>0$$

And in this case the question
$$x-y>0$$ , $$x>y$$ ?
given that x is positive, y is negative is TRUE
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Re: Inequality   [#permalink] 24 Mar 2013, 11:16
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