Equations and how to do them

Question

Solve $$\frac{1}{3n}=\frac{3}{4(2n-1)}$$ please explain how to do this and why you have to change signs from positive to negative or vise versa.

Answer 1

Taking the reciprocal of each side yields:

$$3n=\frac{4}{3}(2n-1)=\frac{8}{3}n-\frac{4}{3}$$

Therefore,

$$\frac{n+4}{3}=0$$

Therefore $n=-4$.

Answer 2

$$\frac {1}{3n}= \frac{3}{4(2n-1)}$$ $$4(2n-1)=9n$$ $$8n-4=9n$$ $$-4=n$$