If x=-|x|, then which one of the following statements

Thanx Bunuel very well explained just tell me if it is x=|x| then what the answer should be
TIA

x = |x| means that x >= 0. So, I and III could be true.
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x = -|x|
Now |x|>=0
-|x|<=0
so x<=0


Answer D

Since x = -|x|, x must be negative or zero. Thus, I and II are true.

Answer: D
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Answer is D

1) If x<0, then x=-|x|=0

2) If x<0 i.e. negative, then x= -(-x) [Here -x is positive because x is less than 0. -ve*-ve= +ve]

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[/quote]

x=-|x|
I. 0=-|0| =0 YES.
II. -1=-|1|
-1=-1 YES.
III. 2=-|2|
2 = -2 NO.
HENCE ANS IS D.

Shiv2016 , in case you are still wondering . . .

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

Then go to my post (same thread) here: WAYS TO THINK ABOUT x = -|x|

Finally, right below mine, Bunuel here: FINISHES THE DISCUSSION

All of them come from this question

I hope they help.
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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

|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.

Therefore, the answer is (D) I and II

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