x:1/3=3/4:1/2

To solve the proportion \( \frac{x}{\frac{1}{3}} = \frac{\frac{3}{4}}{\frac{1}{2}} \), we can cross-multiply or simplify the right side first.

First, simplify \( \frac{\frac{3}{4}}{\frac{1}{2}} \):

\[ \frac{\frac{3}{4}}{\frac{1}{2}} = \frac{3}{4} \times \frac{2}{1} = \frac{3 \times 2}{4 \times 1} = \frac{6}{4} = \frac{3}{2} \]

Now, the equation simplifies to:

\[ \frac{x}{\frac{1}{3}} = \frac{3}{2} \]

Next, we can multiply both sides by \( \frac{1}{3} \):

\[ x = \frac{3}{2} \times \frac{1}{3} = \frac{3 \times 1}{2 \times 3} = \frac{1}{2} \]

Thus, the solution is:

\[ x = \frac{1}{2} \]