This is a trivial question, yet I have only really thought about it today and would like some insight.
To find the $x$-intercept of the following function:
$$f(x) = 2 \sin x + 1$$
We set $f(x) = 0$, subtract $1$ from both sides, divide by $2$ and get the answer: $\sin x= -\frac 12 $.
But if we divide by $2$ first, then subtract $1$, we get the answer: $\sin x = -1$.
How do we know which operation to "undo" first in order to obtain the correct result?