Answer
$8$
Work Step by Step
Recall:
An inverse variation is represented by the equation $xy=k$, where $k$ is the constant of variation.
As the value of $x$ increases, the value of $y$ decreases.
The equation that models the inverse variation can be determined by finding the value of $k$:
This can be done by taking any ordered pair $(x, y)$ then substituting the values of $x$ and $y$ into the inverse variation formula $xy=k$.
Since the variation contains the point $\left(4, 6\right)$, substitute these into the formula $xy=k$ to obtain:
\begin{align*}
xy&=k\\\\
4(6)&=k\\\\
24&=k\\\\
\end{align*}
Thus, the equation of the inverse variation is $xy=24$.
To find the value of $x$ when $y=3$, substitute $3$ to $y$ in the equation above to obtain:
\begin{align*}
xy&=24\\\\
x(3)&=24\\\\
\frac{x(3)}{3}&=\frac{24}{3}\\\\
x&=8\end{align*}
