1. **State the problem:** Write the expression $\frac{4n}{5} - 2 + \frac{3n}{5}$ as a single fraction in simplest form. 2. **Identify the terms:** The expression has two fractions with denominator 5 and a whole number $-2$. 3. **Rewrite the whole number as a fraction:** To combine all terms, write $-2$ as $\frac{-2 \times 5}{5} = \frac{-10}{5}$. 4. **Combine all fractions:** $$\frac{4n}{5} + \frac{3n}{5} + \frac{-10}{5} = \frac{4n + 3n - 10}{5}$$ 5. **Simplify the numerator:** $$4n + 3n - 10 = 7n - 10$$ 6. **Final expression:** $$\frac{7n - 10}{5}$$ 7. **Check simplification:** The numerator and denominator have no common factors, so this is the simplest form. **Answer:** $$\frac{7n - 10}{5}$$