1. **State the problem:** Solve the equation $4 + 3(p - 13) = 7$ for $p$. 2. **Apply the distributive property:** Multiply 3 by each term inside the parentheses: $$4 + 3p - 39 = 7$$ 3. **Combine like terms:** Simplify the left side by combining $4$ and $-39$: $$3p - 35 = 7$$ 4. **Isolate the term with $p$:** Add 35 to both sides: $$3p - 35 + 35 = 7 + 35$$ $$3p = 42$$ 5. **Solve for $p$:** Divide both sides by 3: $$\frac{\cancel{3}p}{\cancel{3}} = \frac{42}{3}$$ $$p = 14$$ 6. **Final answer:** $p = 14$