X:1/3=3/4:1/2

To solve the equation \( \frac{x}{\frac{1}{3}} = \frac{\frac{3}{4}}{\frac{1}{2}} \), we can simplify both sides. First, let's simplify the right side: \[ \frac{\frac{3}{4}}{\frac{1}{2}} = \frac{3}{4} \times \frac{2}{1} = \frac{3 \times 2}{4 \times 1} = \frac{6}{4} = \frac{3}{2} \] Now, we can rewrite the original equation with this simplification: \[ \frac{x}{\frac{1}{3}} = \frac{3}{2} \] To eliminate the fraction on the left side, we can multiply both sides by \( \frac{1}{3} \): \[ x = \frac{3}{2} \times \frac{1}{3} \] Calculating the right side: \[ x = \frac{3 \times 1}{2 \times 3} = \frac{3}{6} = \frac{1}{2} \] Thus, the value of \( x \) is: \[ \boxed{\frac{1}{2}} \]