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Help me out with this (1/x)<x<1

  1. Jun 14, 2008 #1
    Hi all ,
    could someone help me out with this
    (1/x)<x<1

    i tried by drawing the graphs
    and separated it in 2 equations
    but the answer that i found was -1<x<1
    is it correct ?
     
  2. jcsd
  3. Jun 14, 2008 #2
    i got a new breakthrough haha
    this equation does not have a solution set

    correct me if i'm wrong
    if first do the first 2 steps of the equation ,it follows that 1/x < x
    therefore x^2>1
    second equation will be that x<1
    therefore there is no solution
    am i correct ?
     
  4. Jun 14, 2008 #3

    tiny-tim

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    Science Advisor
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    Hi garyljc! :smile:
    Nope! :smile:

    Hint: If a < b and c < 0, is ac < bc? :wink:
     
  5. Jun 14, 2008 #4
    1/x<x
    1/x - x<0
    (1-x^2)/x<0
    (x^2 - 1)/x>0

    case 1: numerator and denominator are positive
    numerator
    x^2-1>0
    (x+1)(x-1)>0
    By wavy curve method
    x<-1 or x>1
    denominator
    x>0
    so solution for this case is x>1
    but x<1 (given in the question)
    hence no solution in this case.

    case 2: numerator and denominator are negative
    x^2-1<0
    (x+1)(x-1)<0
    By wavy curve method
    -1<x<1
    x<0
    so solution for this case is -1<x<0
    but x<1
    hence solution for this case is -1<x<0

    SO THE ANSWER IS -1<X<0
     
  6. Jun 15, 2008 #5
    thanks to both lizzie and tim
     
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