Problem with getting variable by itself in fraction.

Question

I have a problem that looks something like this:

The difference of the quotient of a number and $-2$ from $12$ is $15$.

So I started off like this:

$12-\displaystyle\frac{x}{-2}=15$

Then I subtracted the $12$ from both sides to get:

$-\displaystyle\frac{x}{-2}=3$

Where would I go on from here?

Answer 1

You can multiply the numerator and denominator by $-1$ to clear the signs, then multiply by $2$ to clear the denominator.

Answer 2

$$-\frac{x}{-2} = 3 \;\; \implies \;\;\not - \frac{x}{\not - 2} = 3\; \;\implies\;\;\frac{x}{2} = 3 \;\;\implies\;\; x = 2\cdot 3 = 6$$

Note that $\;-\dfrac{x}{2} = \dfrac{-x}{-2} = \dfrac{-1\cdot x}{-1\cdot 2}$ and now we can cancel $-1$ from both numerator and denomintor, or else mutltiply the numerator and denominator by $-1$; either way, it leaves us with just $\dfrac{x}{2}$.