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Thread: Is this right method?

  1. #1
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    Is this right method?

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    1/5 < 1/(x+1) < 1/2

    Can I write this inequality as this?

    1/(5-1)<1/(x+1-1)<1/(2-1)

    => 1/4<1/x<1/1
    => 4>x>1

    => 1<x<4

    Hence the values 'x' might be '2' and '3'.

    Thanks for your help.

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    An Urch Guru Pundit Swami Sage Makumajon's Avatar
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    Here it works, not because of the possibility of -1 in the first step but because of the inversion in the third step.

    1/5 < 1/(x+1) < 1/2. Well, you see if you can invert 1/(x+1), you can easily solve it. But before inverting inequality, you must check all parts of the inequality to ensure that none can be negative. Here 1/5, 1/2 cannot be negative. So, 1/(x+1) also cannot be. Hence, you can safely invert the inequality by reversing the sign:

    5>(x+1)>2. If you find a variable portion can be negative or positive, you must stop inverting.

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    Thanks a lot buddy.

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    thanks makumajon

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    thanx a lot..................

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