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Is x < 0 ? (1) -4x < 0 (2) -4x^2 < 0

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Is x < 0 ? (1) -4x < 0 (2) -4x^2 < 0 [#permalink] New post 03 Jul 2012, 22:30
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Is x < 0 ?

(1) -4x < 0
(2) -4x^2 < 0


What I want to know is

1) -4x < 0 ; either 4 is negative or x is negative. Hence cant say if x <0.
But explanation for this is given that
dividing both sides by -4, we get x > 0. Hence we know that x > 0.
Can anyone please help me understand why -4x is not 4 * (-x)? and in case it is 4*(-x) then why cant x<0 ?

2) Is clear to me. Hence no questions
[Reveal] Spoiler: OA
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Re: Help clear concept [#permalink] New post 03 Jul 2012, 22:59
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jayoptimist wrote:
Q) Is x < 0 ?
1) -4x < 0
2) -4x^2 < 0

What I want to know is

1) -4x < 0 ; either 4 is negative or x is negative. Hence cant say if x <0.
But explanation for this is given that
dividing both sides by -4, we get x > 0. Hence we know that x > 0.
Can anyone please help me understand why -4x is not 4 * (-x)? and in case it is 4*(-x) then why cant x<0 ?

2) Is clear to me. Hence no questions

Hi,

-4x<0,
if x < 0, let say, x=-1, then (-4)(-1)>0
which contrary to the given inequality.

again, if x>0, let say, x=2, then (-4)(2)<0
Thus, we can say x>0

Let me know if you need any further clarification,

Regards,
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Re: Is x < 0 ? (1) -4x < 0 (2) -4x^2 < 0 [#permalink] New post 04 Jul 2012, 00:32
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Expert's post
jayoptimist wrote:
Is x < 0 ?

(1) -4x < 0
(2) -4x^2 < 0


What I want to know is

1) -4x < 0 ; either 4 is negative or x is negative. Hence cant say if x <0.
But explanation for this is given that
dividing both sides by -4, we get x > 0. Hence we know that x > 0.
Can anyone please help me understand why -4x is not 4 * (-x)? and in case it is 4*(-x) then why cant x<0 ?

2) Is clear to me. Hence no questions


Is x < 0 ?

(1) -4x < 0. Divide both parts by -4 and flip the sign of the inequality since we are dividing by negative number: x>0. Sufficient. (Or just rewrite as 4x>0, which also leads to x>0)

(2) -4x^2 < 0 --> x^2>0. This inequality holds true for positive as well as negative values of x. Not sufficient.

Answer: A.

As for your question: we CAN write -4x < 0 as 4*(-x) < 0. Now, from 4*(-x) < 0 we have that the product of the positive number 4 and -x is negative, so -x must be negative: -x<0 --> x>0.

Hope it's clear.

P.S. Please read and follow: rules-for-posting-please-read-this-before-posting-133935.html
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Intern
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Re: Is x < 0 ? (1) -4x < 0 (2) -4x^2 < 0 [#permalink] New post 04 Jul 2012, 00:55
Thanks Bunuel. I got it!
Re: Is x < 0 ? (1) -4x < 0 (2) -4x^2 < 0   [#permalink] 04 Jul 2012, 00:55
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