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Math Help - Modulus and inequalities

  1. #1
    Junior Member
    Joined
    May 2008
    Posts
    61

    Modulus and inequalities

    Solve this,
    (|x|+1)/(|x|-1)<4

    Is there anything wrong with this step,
    |x|+1 < 4|x|-4 ??
    Then, -3|x|<-5
    |x|>5/3
    x>5/3, x<-5/3

    OR
    when x<0
    (-x+1)/(-x-1)<4
    x<-5/3
    when x>=0
    x>5/3

    But there is another solution of -1<x<1. How to get this out??

    Thanks.
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  2. #2
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
    Posts
    288
    Question
    \frac{|x|+1}{|x|-1}<4

    Instead of multiplying by |x|-1, multiply by (|x|-1)^2 and you should obtain that missing solution when solving the equation.

    This works because when multiplying by |x|-1, you reduce the equation to a linear equation, eliminating possible solutions.
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