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I have a question about basic algebra. Ofcourse, you can add something to both sides to make the equation hold true, but where can you not?

Here for example: $10x(3)=10$ and adding 10 to both sides $10x(3+10)=20$ is not going to hold true. Is there like a list I could look at for those kinds of rules?

I'm watching a video of a teacher explaining how to solve a quadratic equation and he just casually adds something to a multiplication and the same on the other side. So I don't really understood how it's possible since on the one side we are not multiplying and on the other we do, that can't really hold the same value?

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    $\begingroup$ Adding 10 to 10x(3) is 10x(3)+10! Be careful with brackets $\endgroup$
    – QuIcKmAtHs
    Commented Jan 5, 2018 at 6:00

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You have to add the same number to both sides. You added $10(10x)$ to one side and $10$ to the other side.

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