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Inequality homework problem

  1. Sep 16, 2012 #1
    1. The problem statement, all variables and given/known data
    [itex]\frac{3x + 1}{2x - 6}[/itex] < 3


    2. Relevant equations



    3. The attempt at a solution

    [itex]\frac{3x + 1}{2(x -3}[/itex] < 3

    [itex]\frac{3x +1}{x - 3}[/itex] < 6

    Assume x < 3

    3x + 1 > 6(x - 3)
    3x + 1 > 6x - 18
    3x + 1 - 6x + 18 > 0
    19 > 3x
    x < 19/3

    No Contradiction.


    Assume x > 3
    3x + 1 < 6x - 18
    3x - 19 > 0
    3x > 19
    x > 19/3

    No Contradiction




    How do I know which set of values to take?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 16, 2012 #2

    uart

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    Science Advisor

    Re: Inequality

    Hi Darth. You need to consider both the assumption and the consequent result in determining the solution region.

    For example {x < 3 and x < 19/3} means that x must be less than 19/3, but also less than 3, but this is equivalent to simply stating x < 3.
     
  4. Sep 16, 2012 #3

    uart

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    Science Advisor

    Re: Inequality

    For your second solution region, x must be greater than 3, but also greater than 19/3. This is equivalent to simply stating [itex] x > \ldots[/itex]. (You fill that one in. :smile:)
     
  5. Sep 16, 2012 #4
    Re: Inequality

    I attempted a different method

    Is the correct answer

    x < 3
    x > 19/3
     
  6. Sep 16, 2012 #5

    uart

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    Science Advisor

    Re: Inequality

    Yes that is correct.

    BTW. What was your "different method". One alternative is to multiply both sides by the square of the denominator, which makes it into a single quadratic inequality.
     
  7. Sep 16, 2012 #6
    Re: Inequality

    Yeah, that was what I did
    Then tested the point
     
  8. Sep 16, 2012 #7

    CAF123

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    Gold Member

    Re: Inequality

    Could also do [tex] \frac{3x+1 - 3(2x-6)}{2x-6}<0 [/tex] simplify and then draw up an algebraic table to see when each of the quantities (3x-19), (2x-6) are negative, zero or positive (or undefined)for values of x less than 3, 3, 3<x<19/3, 19/3 and greater than 19/3.
     
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