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Re: If x=-|x|, then which one of the following statements [#permalink]

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25 Jun 2017, 23:07

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Re: If x=-|x|, then which one of the following statements [#permalink]

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26 Jun 2017, 00:58

If x = - |x| , then which one of the following statements could be true?

\(x = - |x|\)

The above equation means:

1. x can be ZERO 2. x can be any negative number

Now lets go the options.

I. x = 0 ===> Holds true based on point (1) above =====> TRUE II. x < 0 ===> Holds true based on point (2) above =====> TRUE III. x > 0 ===> Not True as value should either be ZERO or Less than ZERO =====> FALSE

Hence, the answer is D _________________

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If x=-|x|, then which one of the following statements [#permalink]

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01 Oct 2017, 11:10

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This post received KUDOS

Shiv2016 wrote:

It would be great if for once someone clear this doubt. I am not able to move to something new in absolute values because of this same doubt. Every time I try to clear it, it becomes worse.

1) If x>=0 then |x|= x

2) If x<0 then |x|= -(-x)= x (in this x is negative now or positive?)

On a different question, about a week after you posted this (sorry, I didn't see your post until just now), someone asked exactly what I think you are asking.

I answered, because, as I wrote, that rule can feel very counterintuitive to me.

I wrote down a few ways to think about what you asked and I highlighted, above. Bunuel then added another important way to think about it. So . . . three posts that address what I think you are asking.

Please, take a look at Bunuel 's post starting HERE

Re: If x=-|x|, then which one of the following statements [#permalink]

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01 Oct 2017, 22:22

genxer123 wrote:

Shiv2016 wrote:

It would be great if for once someone clear this doubt. I am not able to move to something new in absolute values because of this same doubt. Every time I try to clear it, it becomes worse.

1) If x>=0 then |x|= x

2) If x<0 then |x|= -(-x)= x (in this x is negative now or positive?)

On a different question, about a week after you posted this (sorry, I didn't see your post until just now), someone asked exactly what I think you are asking.

I answered, because, as I wrote, that rule can feel very counterintuitive to me.

I wrote down a few ways to think about what you asked and I highlighted, above. Bunuel then added another important way to think about it. So . . . three posts that address what I think you are asking.

Please, take a look at Bunuel 's post starting HERE

Thank you so much for your reply. Your posts and Bunuel's posts are to the point and cleared all my doubts related to negative sign. I again solved the question. I hope the reasoning makes sense now

Re: If x=-|x|, then which one of the following statements [#permalink]

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13 Oct 2017, 07:32

GMATMadeeasy wrote:

If x = - |x| , then which one of the following statements could be true?

I. x = 0 II. x < 0 III. x > 0

(A) None (B) I only (C) III only (D) I and II (E) II and III

|x| is always positive. Putting a negative sign infront of a positive sign makes the value a negative. So, the value of x is negative. X CANNOT be greater than zero, because this would make x a positive, which would make - |x| a negative, which contradicts the given equation. X could be zero, because the absolute value of zero is zero, and the negative sign does not change the value of zero; therefore, 0 = - |0| holds true.