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# Inequality

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Manager
Joined: 24 Jul 2010
Posts: 88

Kudos [?]: 12 [0], given: 43

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24 Mar 2013, 12:00
How would you solve different scenarios for this inequality algebraically (not with number substitution):

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

Kudos [?]: 12 [0], given: 43

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1120

Kudos [?]: 2370 [1], given: 219

Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

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24 Mar 2013, 12:16
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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Kudos [?]: 2370 [1], given: 219

Re: Inequality   [#permalink] 24 Mar 2013, 12:16
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