1. **State the problem:** Simplify the expression $$\frac{3}{5}x + 19 - \frac{3}{20}x - 7$$. 2. **Combine like terms:** Group the terms with $x$ and the constant terms separately. $$\left(\frac{3}{5}x - \frac{3}{20}x\right) + (19 - 7)$$ 3. **Find a common denominator for the $x$ terms:** The denominators are 5 and 20. The least common denominator is 20. Rewrite $$\frac{3}{5}x$$ as $$\frac{12}{20}x$$. 4. **Subtract the $x$ terms:** $$\frac{12}{20}x - \frac{3}{20}x = \frac{12 - 3}{20}x = \frac{9}{20}x$$ 5. **Simplify the constants:** $$19 - 7 = 12$$ 6. **Write the simplified expression:** $$\frac{9}{20}x + 12$$ **Final answer:** $$\frac{9}{20}x + 12$$