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# If x is different from 0, is |x| < 1 ?

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Joined: 02 Sep 2009
Posts: 49320
Re: If x is different from 0, is |x| < 1 ?  [#permalink]

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09 Mar 2018, 23:46
shiying wrote:
Bunuel wrote:
carcass wrote:
I suppose that you have put in red my logic on stat 1 because not so clear.

Stat (1) : x > 1 or -x > 1.........x < -1

Stat (2) : x < x or -x > x.........x < -x

This is the logic that conduct me to say that the 2 stats are insufficient. I don't understand completely why in the 2 one |x| > x ........ x is < 0 ??'

I also read the topic that you suggested; your third reply is very helpful but the doubt remain on stat ( 2)

Thanks

OK. First of all: I marked "|x|<1" in red for (1), because you don't get that |x| < 1 from this statement. If it were so then then you'd have an YES answer right away (as the question asks exactly about the same thing "is |x|<1")

Next, "is $$|x|<1$$?" means "is $$-1<x<1$$?"

(1) x*|x|<x holds true in two cases for $$x<-1$$ and $$0<x<1$$:
-----(-1)----(0)----(1)----
So as you can see this one is not sufficient to answer the question.

Hope it's clear.

Hi Bunuel, can x also be x>-1 for Statement 1? Coz when I sub in the values of (-1/2) or (-1/4), x satisfies the equation. But on your number line it is in black, which indicates x>-1 does not hold true. Please kindly enlighten me.

Neither of these values satisfies x*|x| < x.

If x = -1/2, then (x*|x| = -1/4) > -1/2 NOT <.
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Re: If x is different from 0, is |x| < 1 ?  [#permalink]

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10 Mar 2018, 00:03
Thank you Bunuel, silly me. my brain must be so fried from all the inequalities.
Re: If x is different from 0, is |x| < 1 ? &nbs [#permalink] 10 Mar 2018, 00:03

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# If x is different from 0, is |x| < 1 ?

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