Ask any scientist or mathematician, and this is the quality that they would love their solution to have. They want the result to be elegant, simple, and intuitive.

At first glance, the answer would be, “no”. However, giving that answer would be missing the point.

Trying to solve the problem all at once is complicated, and usually too messy. When trying to solve something in one step, it’s easy to make mistakes or otherwise fail. It’s the nature of trying to figure out faster ways to perform tasks.

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As I was tutoring one of my students about algebra, I could see that he was struggling with making sense of the rules of how to manipulate equations in order to solve for a given variable. The equation involved fractions and like terms, and looked something like this: