Answer
$x = \frac{1}{6}$
Work Step by Step
Our equation for an inverse variation is $y = \frac{k}{x}$ or $xy = k$ or, as will be needed in this problem, $x = \frac{k}{y}$. We will use the second form of the equation to solve for k.
We use the ordered pair (\frac{1}{3},\frac{1}{4}) to solve for k, from which we know that $x = \frac{1}{3}$ and $y = \frac{1}{4}$.
$\frac{1}{3}\times\frac{1}{4}= k$
$ \frac{1}{12} = k$
So, $k = \frac{1}{12}$
Therefore, our equation for the inverse variation is $y = \frac{\frac{1}{12}}{x}$ or $xy = \frac{1}{12}$ or $x = \frac{\frac{1}{12}}{y}$
Using the third form of the equation, $x = \frac{\frac{1}{12}}{y}$, we can use the y value of the second order pair to find our missing x value.
$x = \frac{\frac{1}{12}}{\frac{1}{2}}$
$x = \frac{1}{6}$
