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Math Help - Simplifying Linear Equations

  1. #1
    Member cmf0106's Avatar
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    Simplifying Linear Equations

    This is some steps into the equation

    But I am having difficulty simplifying this
    x- \frac{3}{2}x = -8\frac{1}{2}

    The author shows the above simplified as
     -\frac{1}{2}x = -8 \frac{1}{2}

    Can you adjust assume X = 1 and do  1 - 3/2 thus equaling -\frac{1}{2}x?
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  2. #2
    Super Member wingless's Avatar
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    Quote Originally Posted by cmf0106 View Post
    Can you adjust assume X = 1 and do  1 - 3/2 thus equaling -\frac{1}{2}x?
    No. It could be -\frac{1}{2}x^5 as well. Well, you could only use this method in a test..

    Anyway,
    x- \frac{3}{2}x = -8\frac{1}{2}

    Factor the x on LHS,
    x\cdot \left ( 1 - \frac{3}{2} \right ) = -8\frac{1}{2}

    x\cdot \left (- \frac{1}{2} \right ) = -8\frac{1}{2}

    -\frac{1}{2}x = -8\frac{1}{2}
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  3. #3
    Member cmf0106's Avatar
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    Thanks for clarifying, that makes perfect sense. However, does LHS mean left hand side of the equation?
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  4. #4
    Super Member wingless's Avatar
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    Quote Originally Posted by cmf0106 View Post
    Thanks for clarifying, that makes perfect sense. However, does LHS mean left hand side of the equation?
    Exactly
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  5. #5
    Member cmf0106's Avatar
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    Actually one last question I forgot to ask yesterday the problem reads

     x + 8 = \frac{3}{2}x - \frac{1}{2}

    Which leads to

    <br />
x= \frac{3}{2}x -8\frac{1}{2}<br />

    I am not certain how the " -8\frac{1}{2}" is created exactly. The RHS reads \frac{3}{2}x - \frac{1}{2} - 8 So I assume you can just do (once you subtract 8 from both sides in the first equation displayed) " -\frac{1}{2} - 8" which in a calculator = -8.5 or  8\frac{1}{2}

    Could some one please clarify, thanks.
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cmf0106 View Post
    Actually one last question I forgot to ask yesterday the problem reads

     x + 8 = \frac{3}{2}x - \frac{1}{2}

    Which leads to

    <br />
x= \frac{3}{2}x -8\frac{1}{2}<br />

    I am not certain how the " -8\frac{1}{2}" is created exactly. The RHS reads \frac{3}{2}x - \frac{1}{2} - 8 So I assume you can just do (once you subtract 8 from both sides in the first equation displayed) " -\frac{1}{2} - 8" which in a calculator = -8.5 or  8\frac{1}{2}

    Could some one please clarify, thanks.
    Your reasoning is correct.

    I find the whole 8 \frac{1}{2} notation hazardous to begin with. Unless you are told otherwise by your instructor I'd advise you to write it as an "improper fraction:"
    8 \frac{1}{2} = 8 + \frac{1}{2} = \frac{17}{2}

    -Dan
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  7. #7
    Member cmf0106's Avatar
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    Thanks for clarifying! Using improper fractions intuitively makes more sense so I appreciate the suggestion.

    And as far as what my instructor does, I am teaching myself algebra all over again to eventually teach myself pre-cal, calculus I, and calculus II before I ever head into the class room.
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