Answer
$x=32$
Work Step by Step
Recall:
A direct variation is represented by the equation $y=kx$, where $k$ is the constant of variation.
As the value of $x$ increases, the value of $y$ also increases.
The equation that models the direct variation can be determined by solving 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 direct variation formula $y=kx$.
Since the variation contains the point $(4, 1.5)$, substitute these into the formula $y=kx$ to obtain:
\begin{align*}
y&=kx\\\\
1.5&=k(4)\\\\
\frac{1.5}{4}&=\frac{k(4)}{4}\\\\
\frac{3}{8}&=k
\end{align*}
Therefore, the equation that models the direct variation is $y=\frac{3}{8}x$.
To find the value of $x$ when $y=12$, substitute $12$ to $y$ in the equation above to obtain:
\begin{align*}
y&=\frac{3}{8}x\\\\
12&=\frac{3}{8}x\\\\
\frac{12}{\frac{3}{8}}&=\frac{\frac{3}{8}}{\frac{3}{8}}x\\\\
32&=x
\end{align*}
