1. **State the problem:** Solve for $x$ in the equation $$\frac{x}{4} - \frac{x}{5} = \frac{7}{20}.$$\n\n2. **Use a common denominator:** The denominators are 4, 5, and 20. The least common denominator (LCD) is 20. Rewrite each term with denominator 20:\n$$\frac{x}{4} = \frac{5x}{20}, \quad \frac{x}{5} = \frac{4x}{20}.$$\n\n3. **Rewrite the equation:**\n$$\frac{5x}{20} - \frac{4x}{20} = \frac{7}{20}.$$\n\n4. **Combine the left side:**\n$$\frac{5x - 4x}{20} = \frac{7}{20} \implies \frac{x}{20} = \frac{7}{20}.$$\n\n5. **Multiply both sides by 20 to clear the denominator:**\n$$\cancel{20} \times \frac{x}{\cancel{20}} = \cancel{20} \times \frac{7}{\cancel{20}} \implies x = 7.$$\n\n6. **Final answer:**\n$$\boxed{7}.$$