Negative Coefficients

In $-3x = 12$, the coefficient of $x$ is $-3$. The unknown was multiplied by negative three. Undo it the same way as any coefficient. Divide both sides by $-3$, with its sign:

$$\frac{-3x}{-3} = \frac{12}{-3}$$

$$x = -4$$

On the left, $-3$ divided by $-3$ is 1, so $x$ is alone. On the right, 12 divided by a negative number is negative, so the answer is $-4$. Check: $-3\cdot \left(-4\right) = 12$.

In $-3x = 12$, dividing both sides by $-3$ gives $x = -4$ in one step. If you divide by 3 instead, you get $-x = 4$, and you still need to multiply both sides by $-1$.