1. **State the problem:** Solve the equation $\frac{1}{2} - \frac{1}{3}p = \frac{3}{4}$ for $p$. 2. **Isolate the term with $p$:** Subtract $\frac{1}{2}$ from both sides: $$\frac{1}{2} - \frac{1}{3}p - \frac{1}{2} = \frac{3}{4} - \frac{1}{2}$$ $$- \frac{1}{3}p = \frac{3}{4} - \frac{2}{4}$$ $$- \frac{1}{3}p = \frac{1}{4}$$ 3. **Solve for $p$:** Multiply both sides by $-3$ to cancel the coefficient: $$p = \cancel{-3} \times \left(\cancel{- \frac{1}{3}} p\right) = -3 \times \frac{1}{4}$$ $$p = - \frac{3}{4}$$ 4. **Final answer:** $$p = - \frac{3}{4}$$ This means the value of $p$ that satisfies the equation is $- \frac{3}{4}$.