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Math Help - Algebra question where the "x" appears twice

  1. #1
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    Algebra question where the "x" appears twice

    Not sure what this kind of question is called, but here it is:

    x10 + (1-x)11 = 10.8

    find x.

    ---

    I know x = 0.2 but the only way I can find it is with trial and error.\
    I have tried shifting terms around but I can not seem to combine the two x's to get a final answer.

    If anyone could write out the steps for solving this that would be great
    You can rearrange it to: 10x + 11(1-x) = 10.8 if you want, I have written it differently for a specific reason but it is not important for solving the question.
    Once again, I can find the answer with trial and error but I don't have time for that in the exam :O

    Thanks in advanced!
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  2. #2
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    Quote Originally Posted by Siddy View Post
    Not sure what this kind of question is called, but here it is:

    x10 + (1-x)11 = 10.8

    find x.

    ---

    I know x = 0.2 but the only way I can find it is with trial and error.\
    I have tried shifting terms around but I can not seem to combine the two x's to get a final answer.

    If anyone could write out the steps for solving this that would be great
    You can rearrange it to: 10x + 11(1-x) = 10.8 if you want, I have written it differently for a specific reason but it is not important for solving the question.
    Once again, I can find the answer with trial and error but I don't have time for that in the exam :O

    Thanks in advanced!
    Expand, simplify, solve.
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  3. #3
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    x10 + (1-x)11 = 10.8
    x10 + 11 -x11 = 10.8
    x10 -x11 = 10.8 -11
    -x1 = -0.2
    x = 0.2

    Thanks!
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  4. #4
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    I assume that since you have written the numbers AFTER the letters, they are actually the powers, i.e. your equation is

    \displaystyle x^{10} + (1 - x)^{11} = 10.8

    Is this correct?

    Edit: I see that it's not. It's convention to usually put the coefficient of x BEFORE the x, then everybody knows that you mean that is a multiple of x and not a power.
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