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Thread: Distributing and simplifying

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    Senior Member vaironxxrd's Avatar
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    Distributing and simplifying

    4(3x-5)= -2(-x+8)

    I got 10x= 4
    = 2.5
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    Re: Distributing and simplifying

    Quote Originally Posted by vaironxxrd View Post
    4(3x-5)= -2(-x+8)

    I got 10x= 4
    = 2.5
    $\displaystyle \displaystyle \begin{align*} 4(3x-5) &= -2(-x+8) \\ 12x-20 &= 2x-16\\ 10x-20 &= -16\\ 10x &= 4 \\ x &= \frac{4}{10} \\ x &= \frac{2}{5}\end{align*}$

    I disagree with your answer of $\displaystyle \displaystyle x = 2.5$
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    Senior Member vaironxxrd's Avatar
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    Re: Distributing and simplifying

    Quote Originally Posted by Prove It View Post
    $\displaystyle \displaystyle \begin{align*} 4(3x-5) &= -2(-x+8) \\ 12x-20 &= 2x-16\\ 10x-20 &= -16\\ 10x &= 4 \\ x &= \frac{4}{10} \\ x &= \frac{2}{5}\end{align*}$

    I disagree with your answer of $\displaystyle \displaystyle x = 2.5$


    Oh so I was pretty close . One more question when 10x/4 you divide by 10 to get x by itself?
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    MHF Contributor Siron's Avatar
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    Re: Distributing and simplifying

    Quote Originally Posted by vaironxxrd View Post
    Oh so I was pretty close . One more question when 10x/4 you divide by 10 to get x by itself?
    Do you mean:
    $\displaystyle \frac{\frac{10x}{4}}{10}$?
    Because that's not just $\displaystyle x$ but $\displaystyle \frac{\frac{10x}{4}}{10}=\frac{x}{4}$
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    Senior Member vaironxxrd's Avatar
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    Re: Distributing and simplifying

    Quote Originally Posted by Siron View Post
    Do you mean:
    $\displaystyle \frac{\frac{10x}{4}}{10}$?
    Because that's not just $\displaystyle x$ but $\displaystyle \frac{\frac{10x}{4}}{10}=\frac{x}{4}$
    So your telling me its basically 10x/4/10? That looks weird
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    Re: Distributing and simplifying

    Quote Originally Posted by vaironxxrd View Post
    Oh so I was pretty close . One more question when 10x/4 you divide by 10 to get x by itself?
    10x/4 has to equal something though. In this case it is equal to 1 because you've brought the 4 from the RHS onto the LHS by division: $\displaystyle \dfrac{10}{4} x = 1$. From here you'd need to divide both sides by 10/4: $\displaystyle x = \dfrac{1}{\left(\frac{10}{4}\right)}$ and since we divide fractions by "flip n multiply" the RHS is the same as $\displaystyle 1 \times \dfrac{4}{10} = \dfrac{4}{10}$



    From the line $\displaystyle 10x = 4$ you can divide both sides by 10 because we want to get x on it's own (which is the same as 1x): $\displaystyle \dfrac{10x}{10} = \dfrac{4}{10}$ and since 10/10 is indeed 1 this is the same as $\displaystyle \dfrac{4}{10}$ which is correct but it's more proper to simplify fractions and so 2/2 was cancelled.

    $\displaystyle \dfrac{4}{10} = \dfrac{2 \times 2}{2 \times 5} = \dfrac{2}{5}$.
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