The Opposite of x

$-x$ means the opposite of x. It is the same as $-x$, a coefficient of $-1$ with the 1 left unwritten, just as $x$ means $x$. So $-x = 7$ is a one-step equation with coefficient $-1$. Divide both sides by $-1$:

$$\frac{-x}{-1} = \frac{7}{-1}$$

$$x = -7$$

There are two ways to solve $-x = 7$, and both give the same answer. You can divide both sides by $-1$. Or you can take the opposite of both sides: the opposite of $-x$ is $x$, and the opposite of 7 is $-7$. Check: the opposite of $-7$ is 7, so $x = -7$ is correct.