1. The problem is to solve for $x$ in the equation $$\frac{1}{2x} + \frac{3}{x} = y.$$\n\n2. To solve for $x$, first find a common denominator for the fractions on the left side. The denominators are $2x$ and $x$, so the common denominator is $2x$.\n\n3. Rewrite the fractions with the common denominator:\n$$\frac{1}{2x} + \frac{3}{x} = \frac{1}{2x} + \frac{3 \times 2}{x \times 2} = \frac{1}{2x} + \frac{6}{2x}.$$\n\n4. Combine the fractions:\n$$\frac{1}{2x} + \frac{6}{2x} = \frac{1 + 6}{2x} = \frac{7}{2x}.$$\n\n5. Now the equation is $$\frac{7}{2x} = y.$$\n\n6. To solve for $x$, multiply both sides by $2x$ to get rid of the denominator:\n$$\cancel{2x} \times \frac{7}{\cancel{2x}} = y \times 2x \Rightarrow 7 = 2xy.$$\n\n7. Divide both sides by $2y$ to isolate $x$:\n$$x = \frac{7}{2y}.$$\n\n8. This is the solution for $x$ in terms of $y$.\n\nFinal answer: $$x = \frac{7}{2y}.$$