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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

    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


    User Avatar
    Science Advisor
    Homework Helper

    Hi garyljc! :smile:
    Nope! :smile:

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

    case 1: numerator and denominator are positive
    By wavy curve method
    x<-1 or x>1
    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
    By wavy curve method
    so solution for this case is -1<x<0
    but x<1
    hence solution for this case is -1<x<0

  6. Jun 15, 2008 #5
    thanks to both lizzie and tim
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