# How do you solve P_1V_1 = P_2V_2 for V_2?

Mar 14, 2016

Divide each side of the equation by ${P}_{2}$.

#### Explanation:

You have been given an algebraic expression:

${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$.

I can perform regular arithmetic operations on this equality, PROVIDED that I do so to both sides. So, if I divide BOTH sides by ${P}_{2}$, I get:

$\frac{{P}_{1} {V}_{1}}{P} _ 2 = \frac{\cancel{{P}_{2}} {V}_{2}}{\cancel{{P}_{2}}}$ $=$ ${V}_{2}$