If x varies inversely as v and x=6 when v=3, then find x when v=9.
$\displaystyle x = \frac{k}{v}$
$\displaystyle x_1 = \frac{k}{v_1}$
$\displaystyle x_2 = \frac{k}{v_2}$
Where $\displaystyle x_1 = 6$, $\displaystyle v_1 = 3$, $\displaystyle v_2=9$
$\displaystyle \frac{x_2}{x_1} = \frac{\frac{k}{v_2}}{\frac{k}{v_1}} = \frac{v_1}{v_2}$
Solve: $\displaystyle x_2 = \frac{x_1 v_1}{v_2}$