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# If |x|=−x, which of the following must be true?

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Manager
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If |x|=−x, which of the following must be true? [#permalink]

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22 Mar 2014, 01:31
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If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x2>x
D. x3<0
E. 2x<x
[Reveal] Spoiler: OA

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Re: If |x|=−x, which of the following must be true? [#permalink]

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22 Mar 2014, 03:24
|x| =-x means absolute value of x is equal to negative of x. Since absolute value cannot be negative hence negative of x should result in a non negative number. It means x is a non positive number i.e. x< 0. Answer is B
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Posts: 43853
Re: If |x|=−x, which of the following must be true? [#permalink]

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22 Mar 2014, 03:39
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Mountain14 wrote:
If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x2>x
D. x3<0
E. 2x<x

When $$x\leq{0}$$ then $$|x|=-x$$, or more generally when $$some \ expression\leq{0}$$ then $$|some \ expression|={-(some \ expression)}$$. For example: $$|-5|=5=-(-5)$$;

When $$x\geq{0}$$ then $$|x|=x$$, or more generally when $$some \ expression\geq{0}$$ then $$|some \ expression|={some \ expression}$$. For example: $$|5|=5$$;

Below posts might help to brush up fundamentals on modulus:
Theory on Abolute Values: math-absolute-value-modulus-86462.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope this helps.
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Re: If |x|=−x, which of the following must be true? [#permalink]

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22 Mar 2015, 07:04
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Re: If |x|=−x, which of the following must be true? [#permalink]

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15 May 2016, 10:44
If x is negative how can x≤0? x<0 is appropriate as 0 is neither negative nor positive.
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Re: If |x|=−x, which of the following must be true? [#permalink]

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15 May 2016, 10:47
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Senthil7 wrote:
If x is negative how can x≤0? x<0 is appropriate as 0 is neither negative nor positive.

x is not negative, it's non-positive. The given equation holds for 0 too. Please check complete solution above.
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Re: If |x|=−x, which of the following must be true? [#permalink]

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04 Apr 2017, 06:04
Bunuel wrote:
Mountain14 wrote:
If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x2>x
D. x3<0
E. 2x<x

When $$x\leq{0}$$ then $$|x|=-x$$, or more generally when $$some \ expression\leq{0}$$ then $$|some \ expression|={-(some \ expression)}$$. For example: $$|-5|=5=-(-5)$$;

When $$x\geq{0}$$ then $$|x|=x$$, or more generally when $$some \ expression\geq{0}$$ then $$|some \ expression|={some \ expression}$$. For example: $$|5|=5$$;

Below posts might help to brush up fundamentals on modulus:

Hope this helps.

By definition of mudulus:
mod(x) = x if x greater than or equal to zero and
mod (x) = -x if x is less than zero....
so we get solution as x<0....therefore x to the power 3 will always be negative or less than zero
What is wrong with D?....put in any negative value of x such as -5 or -0.5 or -1 we always get less than zero value.

Is there anything wrong in the abive stated definition of modulus that we learned in high school. I agree B also serves the purpose but then what about the definition...i mean wrong fundamentals were taught????
Math Expert
Joined: 02 Sep 2009
Posts: 43853
Re: If |x|=−x, which of the following must be true? [#permalink]

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04 Apr 2017, 06:29
Expert's post
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saurabhsavant wrote:
Bunuel wrote:
Mountain14 wrote:
If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x2>x
D. x3<0
E. 2x<x

When $$x\leq{0}$$ then $$|x|=-x$$, or more generally when $$some \ expression\leq{0}$$ then $$|some \ expression|={-(some \ expression)}$$. For example: $$|-5|=5=-(-5)$$;

When $$x\geq{0}$$ then $$|x|=x$$, or more generally when $$some \ expression\geq{0}$$ then $$|some \ expression|={some \ expression}$$. For example: $$|5|=5$$;

Below posts might help to brush up fundamentals on modulus:

Hope this helps.

By definition of mudulus:
mod(x) = x if x greater than or equal to zero and
mod (x) = -x if x is less than zero....
so we get solution as x<0....therefore x to the power 3 will always be negative or less than zero
What is wrong with D?....put in any negative value of x such as -5 or -0.5 or -1 we always get less than zero value.

Is there anything wrong in the abive stated definition of modulus that we learned in high school. I agree B also serves the purpose but then what about the definition...i mean wrong fundamentals were taught????

D is not always true because it implies that x is negative, while |x|=−x stands true for negative numbers as well as for 0.
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Re: If |x|=−x, which of the following must be true?   [#permalink] 04 Apr 2017, 06:29
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