Final answer:
When y varies inversely as x, we can use the initial values of y and x to find the constant of variation and then solve for the unknown variable. In this case, when y = 12, x = -2.
Step-by-step explanation:
When y varies inversely as x, it means that y and x are related by the equation k = ⁻ k/x, where k is a constant. To find the value of x when y = 12, we can use the initial values of y = 8 and x = 3 to find the value of k. Plugging these values into the equation, we have 8 = ⁻ k/3. Solving for k, we get k = 24. Then we can substitute k and y = 12 into the equation to find x: 12 = ⁻ 24/x. Rearranging the equation, we get 12x = ⁻ 24, and solving for x, we find x = -2.