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Homework Help: Inequality Solution [ , +Part solution included]

  1. Sep 25, 2010 #1
    Inequality Solution [URGENT, +Part solution included]

    1. The problem statement, all variables and given/known data


    l 3/(x-1) - 5 l < 4

    2. Relevant equations



    3. The attempt at a solution

    so heres where im abit confused. since the inequality sign is not > or >= but instead in this case it is <. Therefore, x has to be between two numbers.

    But when i tried to solve l 3/(x-1) - 5 l < 4, it doesnt work out.
    Heres my work:

    -4 < 3/(x-1) - 5 < 4
    1 < 3/(x-1) < 9
    x-1 < 3 < 9x-9

    you see.. this is nothing where its suppose to be.
    i end up getting... bigger number < x < smaller number

    am i going the wrong way? please help !
     
  2. jcsd
  3. Sep 25, 2010 #2
    Re: Inequality Solution [URGENT, +Part solution included]

    Use the fact that if
    [tex] a < \frac{1}{x} < b[/tex]

    then

    [tex] \frac{1}{a} > x > \frac{1}{b}[/tex] .
     
  4. Sep 25, 2010 #3
    Re: Inequality Solution [URGENT, +Part solution included]

    well heres a better question.

    can i make the equation like this ?

    1 < 3(x-1) < 9
    x-1<3 or 3<9x-9
    x < 4 or x > 4/3

    Can this work too? 4/3 < x < 4
     
  5. Sep 25, 2010 #4
    Re: Inequality Solution [URGENT, +Part solution included]

    You can do that, but that method will be confusing if you ever work with inequalities that have unknowns instead of numbers.
     
  6. Sep 25, 2010 #5
    Re: Inequality Solution [URGENT, +Part solution included]

    Clarification:

    [tex]a<\frac{1}{x}<b[/tex]
    [tex]\implies\frac{1}{a}>x>\frac{1}{b}[/tex]

    is only necessarily true if a and b are both negative or both positive. Sorry for the error.
     
  7. Sep 25, 2010 #6

    Mark44

    Staff: Mentor

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