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Math Help - Are These 2 Linear Equations Correct?

  1. #1
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    Are These 2 Linear Equations Correct?

    The First One: 8(5-3x)-4(2+3x)=3

    Expansion: -24x -12x 40-8 =3

    Combine:-36x 32 =3

    Shift: -36x = 3-32= -29

    Solution: x= -29/-36

    The Second One: 9(1+x)-8(x+2)= 2x

    Expansion: 9x-8x 9-16 =2x

    Combine: x -7 =2x

    Shift: (x-2x) -7= 2x -2x

    -x = -7

    Solution: x= -7/-1

    Is my formula for solving these equations correct (there are other ways but I thought my method is the easiest, or am I wrong?)? And are my solutions correct? If they're wrong, could you show me where I went wrong? Thanks guys!
    Last edited by MathClown; November 4th 2012 at 01:56 AM.
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  2. #2
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    Re: Are These 2 Linear Equations Correct?

    These are very hard to read as you keep forgetting plus and minus signs! But your logic is fine. The first is correct. The second is not.

    You are correct up to \displaystyle \begin{align*} x - 7 = 2x \end{align*}, now subtract \displaystyle \begin{align*} x \end{align*} from both sides to find \displaystyle \begin{align*} -7 = x \end{align*}.
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    Re: Are These 2 Linear Equations Correct?

    Quote Originally Posted by Prove It View Post
    These are very hard to read as you keep forgetting plus and minus signs! But your logic is fine. The first is correct. The second is not.

    You are correct up to \displaystyle \begin{align*} x - 7 = 2x \end{align*}, now subtract \displaystyle \begin{align*} x \end{align*} from both sides to find \displaystyle \begin{align*} -7 = x \end{align*}.
    For the second one, WolframAlpha says the answer is x=7/-1???
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  4. #4
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    Re: Are These 2 Linear Equations Correct?

    Quote Originally Posted by MathClown View Post
    For the second one, WolframAlpha says the answer is x=7/-1???
    Which is equal to -7...
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    Re: Are These 2 Linear Equations Correct?

    Quote Originally Posted by Prove It View Post
    Which is equal to -7...
    So WolframAlpha got it wrong? The final simplified answer is just x=-7? Is that what you're getting at? Or simply -7 since you're subtracting both x variables.
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    Re: Are These 2 Linear Equations Correct?

    Quote Originally Posted by MathClown View Post
    So WolframAlpha got it wrong? The final simplified answer is just x=-7? Is that what you're getting at? Or simply -7 since you're subtracting both x variables.
    Remember that when positive number is divided or multiplied by negative number, answer is negative. Wolfram alpha gave you \frac{7}{-1}=-7. So both Wolfram Alpha and Prove It are correct.
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