1. **State the problem:** 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:** $$2p + 10 = 6p - 3$$ 4. **Bring all terms involving $p$ to one side and constants to the other:** $$2p + 10 = 6p - 3$$ Subtract $2p$ from both sides: $$\cancel{2p} + 10 = 6p - 3 - \cancel{2p}$$ $$10 = 4p - 3$$ 5. **Add 3 to both sides to isolate the term with $p$:** $$10 + 3 = 4p - 3 + 3$$ $$13 = 4p$$ 6. **Divide both sides by 4 to solve for $p$:** $$\frac{13}{\cancel{4}} = \frac{4p}{\cancel{4}}$$ $$p = \frac{13}{4}$$ **Final answer:** $$p = \frac{13}{4}$$