I understand $-x$ to be the additive inverse of $x$ and vice versa. But looking at an example in my book, it says $-x$ = $-(x)$. Is that quite literally a result of the fact that negative $x$ is equal to the negation of $x$ or is there an alternative reasoning to it?
It's just multiplicative associative property. $$-x=-1\cdot x$$ And by the aforementioned property, $$-1\cdot x=-(x)$$ Thus, $$-x=-(x)$$