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Inside you there are two equations
(hexbear.net)
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this post was submitted on 28 Oct 2024
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chapotraphouse
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2(1 + 2) does imply multiplication: 2 * (1 + 2). The reason it counts as one term, as I noted below, is because it is inside a two-dimensional fraction which has implicit parathenses in the numerator, denominator, and the fraction itself. The first equation is actually ((6) / (2(1 + 2))). When a fraction is written in two dimensions instead of a single string, the division between the numerator and the denominator is supposed to be done last.
The first equation is not 6 / 2(1 + 2). If it was, this means you get (6 / 2) * (1 + 2) as in the second equation, which means (1 + 2) is moved up to the numerator ((6(1+2)) / 2 = (6 / 2) * (1 + 2)), which means the two problems are not equal to each other. I believe this is the point of the "joke".
2x still means 2 * x.
https://www.wolframalpha.com/input?i=6%2F2x
x is still multiplied last. There's not a rule for implied multiplication shorthand preceding operations to the left. You still need to wrap 2x in parentheses if you want the operation to occur first.
https://www.wolframalpha.com/input?i=6%2F%282x%29
This isn't like a polynomial like ax^2 + bx + c as division is done between 6 and 2 before multiplication with x. Typically you wouldn't see such an equation (which is intended to trick you) as normally addition or subtraction would occur like in a polynomial or another variable equation (such as a linear graph), which would be done after the exponents, multiplication, and division with the variables are calculated. In the instance you wrote, it should be written as (6/2)x, or 3x, to avoid obscuring the equation. Though you intended for 6/(2x), or 3/x.
And no worries, comrade, I'm just meaning to help since I am good at math and like helping people (I don't mean this in an egotistical way). I'm not taking offense, and I am not meaning to offend anyone.