> "x + 1 = 6" I didn't have to subtract 1 from each side, I just thought about it logically and knew the answer. I don't see the difference. In my mind, thinki

> "x + 1 = 6" I didn't have to subtract 1 from each side, I just thought about it logically and knew the answer. I don't see the difference. In my mind, thinking about it logically is recognizing that one side has an excess and removing it from the other side. That's subtracting. To you is it like looking at 5 * 4 and knowing it's 20 rather than thinking about 2 * 5 is 10 and two of those is 20? I was the kind of rule-following kid who went through the algebra steps because you were supposed to rather than out of necessity. (Or so I like to think: I'm not good at math in my head because I always wrote it out or maybe I relied on paper since I couldn't do it in my head.) I recall rebelling against memorizing multiplication tables in grade ~4 because I thought my time was better spent leaning new stuff (or maybe understanding how to multiply faster -- wouldn't that be ironic!). It's always interesting to hear how someone else's brain works. Thank you.