1. **State the problem:** We need to find the value of $p$ such that the expressions $2(p + 5)$ and $3(2p - 1)$ are equal. 2. **Write the equation:** $$2(p + 5) = 3(2p - 1)$$ 3. **Apply the distributive property:** $$2 \times p + 2 \times 5 = 3 \times 2p - 3 \times 1$$ $$2p + 10 = 6p - 3$$ 4. **Bring all terms involving $p$ to one side and constants to the other:** $$2p + 10 = 6p - 3$$ $$2p - 6p = -3 - 10$$ $$\cancel{2p} - \cancel{6p} = -13$$ $$-4p = -13$$ 5. **Divide both sides by $-4$ to solve for $p$:** $$p = \frac{-13}{-4}$$ $$p = \frac{13}{4}$$ 6. **Final answer:** $$p = \frac{13}{4}$$ This means when $p = \frac{13}{4}$, the two expressions are equivalent.