Do negative signs count as subtraction or multiplication?

Question

Would $-x$ count as $0 - x$ or $(-1)\times x$?

Answer 1

Usually $-x$ is defined as that number satisfying $x+(-x) = 0$, and subtraction is defined as $a-b = a+(-b)$. Whatever the definitions, it is true that $-x = 0 - x = (-1) \cdot x$.

Answer 2

Seems that to define $-x$ as $-1*x$ you would first have to have a definition of $-1$, which would take the form of $-1$ is that number for which $1 + (-1) = 0$, or in general, $x + (-x) = 0$.

In order to define it as $0 - x$ you would again first have to define what "-" means, and you'd come back to that $x - x = 0$.