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Which of the following inequalities is equivalent to

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Which of the following inequalities is equivalent to [#permalink] New post   12 Aug 2018, 03:18
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Which of the following inequalities is equivalent to \(-\frac{a}{3b} < c\) for all non-zero values of a, b, and c?

Indicate all such inequalities.

A. \(\frac{a}{b} > -3c\)

B. \(\frac{-a}{3} < bc\)

C. \(a > -3bc\)
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Re: Which of the following inequalities is equivalent to [#permalink] New post   12 Aug 2018, 03:59
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Carcass wrote:
Which of the following inequalities is equivalent to \(-\frac{a}{3b} < c\) for all non-zero values of a, b, and c?

Indicate all such inequalities.

A. \(\frac{a}{b} > -3c\)

B. \(\frac{-a}{3} < bc\)

C. \(a > -3bc\)


Here

\(-\frac{a}{3b} < c\)

or we can write as : \(\frac{a}{b} > -3c\) which is the only correct answer and is always true.

For the option B and option C, we donot know the sign of the variable b and c. They could be either positive or negative. So we cannot assume to be positive unless it is mentioned.

Hence option A is the only correct answer
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Re: Which of the following inequalities is equivalent to [#permalink] New post   13 Jun 2019, 08:33
as because of the non-zero character of a,b,c option B and C are not correct.
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Re: Which of the following inequalities is equivalent to [#permalink] New post   21 Aug 2019, 19:02
"or we can write as : ab>−3cab>−3c which is the only correct answer and is always true."

It might be also the case that that either a or b are negative and that will complement the negative. And then when you are shifting it to the other side of the inequality, that will change the relation from ">" to "<" . So, I thing (perhaps, one answer should be right) the above may not be assured. Any one can help me solve this perplexity?
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Re: Which of the following inequalities is equivalent to [#permalink] New post   22 Aug 2019, 00:45
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The explanation provided by Pranab is perfect.

In the inequality manipulation, you can only move on the other side the 3.

The other variables NO because you do not know the sign.

I hope is now more clear.

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Re: Which of the following inequalities is equivalent to [#permalink] New post   16 Jun 2022, 20:10
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Re: Which of the following inequalities is equivalent to [#permalink]
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