If x \ne 0 and \frac{x}{|x|} \lt x , which of the following must be true? A. x \gt 1 B. x \gt -1 C. |x| \lt 1 D. |x| > 1 E. -1 \lt x \lt 0

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Bunuel

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12 Dec 2024, 14:56

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Bunuel

How is it that X/−X < X simplifies to −1 < X? Can you please elaborate on that?

Thanks in Advance!

x/(-x) < x

Reduce x's on the left hand side:

1/(-1) < x

-1 < x.

Hope it helps.

thisisakr

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20 Mar 2025, 22:42

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I understand the question however i am curious understand what scenario will option E be correct. like what will be the language or question statement for that scenario?

Bunuel

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20 Mar 2025, 23:50

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thisisakr

I understand the question however i am curious understand what scenario will option E be correct. like what will be the language or question statement for that scenario?

Option E would be correct if the question were phrased as "...which of the following could be true?" However, in that case, other options will also be correct, so it wouldn’t be the only valid choice.

adarsh2209

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24 Sep 2025, 07:30

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I like the solution - it’s helpful.

VenkataSai

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26 Jul 2026, 09:13

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Hi Bunel,
After the edit i have one query.
what if the value of x=1.
the the equation becomes 1<1, which is not true.

So I believe the answer must be 1>x>-1 U x>1. or X>-1 -(1).

Bunuel

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Bunuel

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26 Jul 2026, 10:07

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VenkataSai

Hi Bunel,
After the edit i have one query.
what if the value of x=1.
the the equation becomes 1<1, which is not true.

So I believe the answer must be 1>x>-1 U x>1. or X>-1 -(1).

You are correct that x = 1 does not satisfy the inequality. The exact solution set is

-1 < x < 0 or x > 1.

However, option B does not claim that every x > -1 works. It only claims that every x satisfying the original inequality must be greater than -1. Therefore, B is still correct.

This has already been explained several times in the thread. Please review the thread and follow the links to similar questions.

Bitan2001

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09 Sep 2026, 18:15

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???1<x<0 or x>1 , the x lies in this range. My doubt is that the question is asking which is must true, not asking for the range. So is it safe to assume that i need to consider the option which covers all the range? Even the option contains some values which will not fall in that range, i.e 0<x<1

chetan2u

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09 Sep 2026, 19:26

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Range cannot have extra values but MUST be true can contain extra values given entire range is included.

Say x is between 1 and 3..

Range is 1 to 3

But MUST be true
A. x is positive
B. x is a real number
C. x>0
D. x<5
And so on

Bitan2001