so, idk if this just came more easily to me or w/e but what was your previous assumption w/r/t the 2(x+2) = 2x+2? like my automatic assumption was that since the 2 could apply to both, you could simplify by dividing it out, what impact does your discovery give you aside from giving you a shortcut? (granted, i haven't taken a math class in like 4 years so maybe the full ramifications aren't clear, but it's 100% possible i'm missing an obvious thing, i did drink 2/3 of a bottle of wine tonight)
oh no I wasn’t starting with 2(x+1) = 2x+2! that’s what I was trying to prove. I was only starting with 2x+2, and trying to factor out the 2 using the commutative/associative properties of equality.
your “divide it out” method? that’s what I was looking to prove. my thing isn’t a shortcut necessarily, but it is more conceptual than “you can factor out a 2 cause I say so” which is what I got in middle school. this way promotes better understanding.
