5

Example: $(x+1)(x−1)=x^2+2x+1$ is an linear equation. I agree with all above answers. I wouldn't say that it is a linear equation, but it reduces to, or it is solved by or any other phrase you want to use instead. Because, I mean, that's the idea right? I feel that the relaxed terminology is not quite accurate, and it might generate confusion when they see ...


4

I don't approve of teaching students unusual meanings for standard terms. If I correctly understand your example, $\sin x=x$ would be a linear equation. And whether $ax^2+bx+c$ is linear depends on whether $b^2=4ac$. The issue becomes worse with polynomials of higher degree. It's not clear to me what you mean by two equations being equal (in "or any ...


3

I think I would tend to disagree with your terminology's bent. The label of the equation speaks to the type of the expression which forms the equation. The type of solution set does not label the equation. Quadratic equations are not differently labeled when they have different solution sets. Furthermore, since there are literally infinitely many equivalent ...


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