Inequality (flipping the sign)

[Stockmoose16]

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).

[logitech]

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

[Stockmoose16]

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.

[cramya]

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!

[cramya]

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