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HarveyS
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If |x| = x, which of the following must be true? 22 Mar 2014, 02:31
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B
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If |x| = −x, which of the following must be true?

A. x ≥ 0
B. x ≤ 0
C. x^2 > x
D. x^3 < 0
E. 2x < x

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If |x| = −x, which of the following must be true?
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B
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Bunuel
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If |x| = x, which of the following must be true? 22 Mar 2014, 04:39
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Mountain14
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
Show more

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: \(|5|=5\);

Answer: B.

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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If |x| = x, which of the following must be true? 22 Mar 2014, 04:24
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|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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If |x| = x, which of the following must be true? 15 May 2016, 11:44
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If x is negative how can x≤0? x<0 is appropriate as 0 is neither negative nor positive.
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If |x| = x, which of the following must be true? 15 May 2016, 11:47
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Senthil7
If x is negative how can x≤0? x<0 is appropriate as 0 is neither negative nor positive.
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x is not negative, it's non-positive. The given equation holds for 0 too. Please check complete solution above.
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If |x| = x, which of the following must be true? 04 Apr 2017, 07:04
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Bunuel
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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

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: \(|5|=5\);

Answer: B.

Below posts might help to brush up fundamentals on modulus:

Hope this helps.
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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????
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If |x| = x, which of the following must be true? 04 Apr 2017, 07:29
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saurabhsavant
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Mountain14
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: \(|5|=5\);

Answer: B.

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????
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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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If |x| = x, which of the following must be true? 10 Mar 2018, 04:58
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HarveyS
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
Show more


|x|=−x holds true when x <= 0.

Hence (B)
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If |x| = x, which of the following must be true? 15 Sep 2018, 03:17
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Bunuel
Mountain14
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: \(|5|=5\);

Answer: B.

Below posts might help to brush up fundamentals on modulus:

Hope this helps.
Show more
But wont this also make X^3<0 or option D true ?
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If |x| = x, which of the following must be true? 19 Oct 2019, 06:06
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Arpitkumar
Bunuel
Mountain14
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: \(|5|=5\);

Answer: B.

Below posts might help to brush up fundamentals on modulus:

Hope this helps.
But wont this also make X^3<0 or option D true ?
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At first sight, yes. However, x could also be 0 in the above equation. 0^3 = 0 and NOT 0^3 < 0 (same for C btw). This is why only B is correct
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If |x| = x, which of the following must be true? 21 Apr 2023, 07:29
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HarveyS
If |x| = −x, which of the following must be true?

A. x ≥ 0
B. x ≤ 0
C. x^2 > x
D. x^3 < 0
E. 2x < x

Show Spoiler
If |x| = −x, which of the following must be true?
Show more

Since |x| = -x, x must be negative or equal to zero. Of the answer choices, only answer choice B has values that are either equal to zero or negative.

Answer: B
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If |x| = x, which of the following must be true? 10 Mar 2025, 05:20
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