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I'm learning Algebra and am curious about some methodological fundamentals here. One, in particular is why the following equation:

6(2x + 1 / 3) = 6(x + 4 / 2) 

results in:

2(2x + 1) = 3(x + 4) 

It's obvious that the distributive property swaps the numerators of the fractions and chooses to use another distributive property to complete the equation. Is there a specific formula for this, and why does it work that way specifically?

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    Maybe you are mistyping $6(2x+1/3)$ instead of $6((2x+1)/3)$? Perhaps what the author wrote is $6\frac{2x+1}{3} = 6\frac{x+4}{2}$?2011-10-07
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    What you wrote is correct if you have $6((2x+1)/3) = 6((x+4)/2)$. But $2x+1/3$ is not the same as $(2x+1)/3)$ and $x+4/2$ is not the same as $(x+4)/2$.2011-10-07

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