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




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Re: If x=−x, which of the following must be true?
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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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Re: If x=−x, which of the following must be true?
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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?
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15 May 2016, 10:47



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Re: If x=−x, which of the following must be true?
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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: \(5=5\); 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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Re: If x=−x, which of the following must be true?
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04 Apr 2017, 06:29
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: \(5=5\); 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???? 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?
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10 Mar 2018, 03:58
HarveyS 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 x=−x holds true when x <= 0. Hence (B)
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Re: If x=−x, which of the following must be true?
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15 Sep 2018, 02:17
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: \(5=5\); 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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