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Two expressions on both sides of the equal sign are equivalent to one of them changing sign when switched over to the other side. For instance:

5x = 3x + 10

Is equivalent to:

5x - 3x = 10

That means that you can very well "combine" them, if you don't forget to switch the sign. As it were, you would be switching it over and combining in a single step.

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Q: Why can't you combine like terms across equal signs?
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