Shikh27 wrote:

Dear Team,

In my opinion the answer for this question should be D

Q) If x is an integer is |x|>1

1.(1-2x)(1+x)<0

2.(1-x)(1+2x)<0

from question stem we have to find out whether x>1 or x<-1

From Statement 1 if we don't multiply by -1 and take critical key points

we have x=-1 and x=1/2

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+ (-1) - 1/2 +

As the inequality has a less than sign so valid region should be -1<x<1/2 so the value is neither greater than 1 nor less than -1 so the answer to the question is no

Similarly from statement 2 x=1 and x=-1/2 and if we take critical key points on a number line

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+ (-1/2) - 1 +

So the valid region for the inequality will be -1/2<x<1 so the value is neither greater than 1 nor less than -1 so the answer to the question will be no and hence according to me Answer should be Option D. Please go through my analysis and let me know where i faltered.

Regards

Hi

Shikh27if you are not multiplying the inequality by -1, then note that coefficient of \(x^2\) in the inequality \((1-2x)(1+x)<0\) will be -1. So when you are plotting the zero points on the number line and assigning the signs to the right of the first root, it should be -ve, matching the coefficient of \(x^2\). so the signs should be -, +, - and you need to choose the negative region, implying x>1/2 or x<-1

hence your highlighted part is incorrect, giving you wrong range.