Suppose that $\alpha$ is inversely proportional to $\beta$. If $\alpha = -6$ when $\beta = 12$, find $\alpha$ when $\beta = -2$.
Inversely proportional here means that the value of alpha x beta is -6*12=-72 for any value of alpha and beta. We use this equation and plug in the given value of beta, -2, into the equation.
alpha x beta =-72
alpha x -2 =-72
alpha = 36.