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Math Help - Builder notation - describe complete solution set

  1. #1
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    Builder notation - describe complete solution set

    Hello Guys first I want to thank the very smart people in here. I only wish you guys could be live to show me how to do some of this stuff.


    5/4 (x-1/2) - 5/3 <4/3

    {X/X __ __}

    Please show me how to do this problem. Thank you very much.
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  2. #2
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    Quote Originally Posted by OneidaFL View Post
    Hello Guys first I want to thank the very smart people in here. I only wish you guys could be live to show me how to do some of this stuff.


    5/4 (x-1/2) - 5/3 <4/3

    {X/X __ __}

    Please show me how to do this problem. Thank you very much.
    At the moment this is unreadable.

    I can't tell if the inequality is

    \frac{5}{4}\left(x - \frac{1}{2}\right) - \frac{5}{3} < \frac{4}{3}

    or

    \frac{5}{4\left(x - \frac{1}{2}\right)} - \frac{5}{3} < \frac{4}{3}.


    Please use brackets where they're needed or else learn LaTeX typesetting.
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  3. #3
    Newbie PxEckx's Avatar
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    Hi, OneidaFL!

    I guess it's this:::

    \displaystyle{\frac{5}{4} \left(x - \frac{1}{2}\right) - \left(\frac{5}{3}\right) < \frac{4}{3} }

    [calculate-the-lowest-common-multiple-(LCM) = 12]

    \displaystyle{\frac{ 15  (12x - 6) - 20}{12} < \frac{16}{12} }

    ['cut'-the-equal-denominators-and-make-the-count!]

    15 (12x - 6) - 20 < 16

    180x - 90 - 20 < 16

    180x < 16 + 90 + 20

    180x < 126

    x < \displaystyle{\frac{126}{180}}

    x < \displaystyle{\frac{7}{10}}


    PS: I just didn't understand what's:::
    {X/X __ __}
    IF it's

    \displaystyle{\frac{x}{x} } = 1

    because

    x < \displaystyle{\frac{7}{10}}

     \displaystyle{\frac{7}{10}} : \displaystyle{\frac{7}{10}} = \displaystyle{\frac{70}{70}} \Rightarrow 1

    Hope It helps!
    Last edited by PxEckx; June 28th 2010 at 06:41 PM.
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  4. #4
    Newbie PxEckx's Avatar
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    Quote Originally Posted by Prove It View Post
    Please use brackets where they're needed or else learn LaTeX typesetting.
    I Agree!!! =D You should try to learn it! I'ts not so difficult, and It'll help you to find the results here!
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  5. #5
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    Thank You so very much

    Not only did you give me an answer, but you are so specific on showing me the details, that I know get it on how to do the fractions on these problems.

    I appreciate your help!
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