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Inequality (flipping the sign)

Expert replies
by Stockmoose16 » Mon Oct 27, 2008 10:28 am
Are you allowed to do the following with an inequality:

1/(k+1)>0

Multiply both sides by K+1

K+1>0

K>-1


... I've seen a couple people do this, and I'm wondering why you can multiply both sides by K+1, since you don't know whether K is positive or negative (which means you wouldn't know whether or not to flip the inequality sign).
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Source: — Data Sufficiency |

by logitech » Mon Oct 27, 2008 10:33 am
No you can't. You are right , you don't know the sign of K+1

But, in this case

1/(k+1)>0

since it is greater than ZERO, it means it needs to be positive. Well 1 is positive so k+1 needs to be POSITIVE as well so the equation remains valid

therefore, k+1 > 0
LGTCH
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by Stockmoose16 » Mon Oct 27, 2008 11:35 am
logitech wrote:No you can't. You are right , you don't know the sign of K+1

But, in this case

1/(k+1)>0

since it is greater than ZERO, it means it needs to be positive. Well 1 is positive so k+1 needs to be POSITIVE as well so the equation remains valid

therefore, k+1 > 0
That is true, but the whole point of multiplying both sides by K+1 is to get K in the numerator, so you can determine whether K is positive or negative. If you already know it's positive, there's no reason to multiply it by K+1.
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by cramya » Mon Oct 27, 2008 6:40 pm
K COULD BE NEGATIVE

K= - .5

still 1/k+1 would be > 0

Like logitech mentioned k+1 has to be positive since 1/k+1 > 0 so mutlplying by k+! (a positive qty) doesnt reverse the inequality

or better yet multiply both sides by

(k+1) ^ 2 - always positive

still end up with
k+1 > 0

Hope this helps!
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by cramya » Mon Oct 27, 2008 6:44 pm
Thinkign about it a litle more, I think u would have to mutpily by

(k+1)^2 (may be thats what u meant in ur first post) if this is a data sufficiency question dealing with k

If u mutliply k+1 on both sides we will end up wiht 1>0

Not usefule info for the actual problem if is dealing with k
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