1. **State the problem:** Solve the equation $$-\frac{1}{5}p + \frac{3}{4}p = 11$$ for $p$. 2. **Combine like terms:** To combine the terms with $p$, find a common denominator for the fractions $-\frac{1}{5}$ and $\frac{3}{4}$. 3. The least common denominator of 5 and 4 is 20. Convert each fraction: $$-\frac{1}{5} = -\frac{4}{20}, \quad \frac{3}{4} = \frac{15}{20}$$ 4. Substitute back: $$-\frac{4}{20}p + \frac{15}{20}p = 11$$ 5. Combine the fractions: $$\left(-\frac{4}{20} + \frac{15}{20}\right)p = 11$$ $$\frac{11}{20}p = 11$$ 6. **Isolate $p$:** Multiply both sides by the reciprocal of $\frac{11}{20}$, which is $\frac{20}{11}$: $$p = 11 \times \frac{20}{11}$$ 7. Simplify by canceling 11: $$p = \cancel{11} \times \frac{20}{\cancel{11}} = 20$$ **Final answer:** $$p = 20$$