1. **State the problem:** Solve for the variable $x$ in the equation $$\frac{1}{3}x = 9$$. 2. **Formula and rules:** To isolate $x$, multiply both sides of the equation by the reciprocal of $\frac{1}{3}$, which is 3. 3. **Intermediate work:** $$\frac{1}{3}x = 9$$ Multiply both sides by 3: $$3 \times \frac{1}{3}x = 3 \times 9$$ Simplify the left side: $$x = 27$$ 4. **Explanation:** Multiplying both sides by 3 cancels out the $\frac{1}{3}$ coefficient on $x$, leaving $x$ alone on one side. The right side becomes $27$ because $3 \times 9 = 27$. **Final answer:** $$x = 27$$