Five times a number is divided by $2$ more than that number. If the result is $6,$ then what was the original number?

Answer 1

Let the original number be $x$. We have the equation $\frac{5x}{x+2}=6$. Multiplying both sides of the equation by $x+2$ gives $5x=6x+12$, so $x=\boxed{-12}$. (The division is valid because we are given that $x \neq -2$, so the denominator is not 0.)