1. **State the problem:** If $\frac{1}{2}$ is added to three times the reciprocal of a number $x$, the result is 1. Find the number $x$. 2. **Set up the equation:** The reciprocal of $x$ is $\frac{1}{x}$. Three times the reciprocal is $3 \times \frac{1}{x} = \frac{3}{x}$. Adding $\frac{1}{2}$ gives: $$\frac{3}{x} + \frac{1}{2} = 1$$ 3. **Solve the equation:** Multiply both sides by the least common denominator $2x$ to clear fractions: $$2x \times \left(\frac{3}{x} + \frac{1}{2}\right) = 2x \times 1$$ $$2x \times \frac{3}{x} + 2x \times \frac{1}{2} = 2x$$ $$\cancel{2x} \times \frac{3}{\cancel{x}} + \cancel{2x} \times \frac{1}{\cancel{2}} = 2x$$ $$6 + x = 2x$$ 4. **Isolate $x$:** $$6 = 2x - x$$ $$6 = x$$ 5. **Answer:** The number is $\boxed{6}$.