I've noticed that a lot of students think that when there is just x in an expression with no coefficient, it is automatically equal to 1. Have you noticed or thought this before?
Sometimes we don't realize how much knowing the origin or background of a word (etymology) will impact our basic understanding of what we are actually saying and doing. Let's look at the breakdown of the word Algebra.
In Algebra, we use letters as variables to represent unknown or missing numbers in expressions and equations. But usually our go-to letter for variable is x. Why is that?
I once heard a podcast episode (about math of course) explaining…