1. **State the problem:** Solve the proportion $$\frac{3}{36} - \frac{4}{27} = \frac{3}{x}$$ for $x$. 2. **Rewrite the equation:** $$\frac{3}{36} - \frac{4}{27} = \frac{3}{x}$$ 3. **Simplify the fractions on the left:** $$\frac{3}{36} = \frac{1}{12}$$ 4. **Find a common denominator for the left side:** The denominators are 12 and 27. The least common denominator (LCD) is 108. 5. **Convert fractions to have denominator 108:** $$\frac{1}{12} = \frac{9}{108}$$ $$\frac{4}{27} = \frac{16}{108}$$ 6. **Subtract the fractions:** $$\frac{9}{108} - \frac{16}{108} = \frac{9 - 16}{108} = \frac{-7}{108}$$ 7. **Set equal to the right side:** $$\frac{-7}{108} = \frac{3}{x}$$ 8. **Cross multiply:** $$-7 \times x = 108 \times 3$$ $$-7x = 324$$ 9. **Solve for $x$:** $$x = \frac{324}{-7} = -\frac{324}{7}$$ 10. **Final answer:** $$x = -\frac{324}{7}$$