1. **State the problem:** Simplify the expression $3 \cdot (5x - 8)$. 2. **Formula and rules:** Use the distributive property: $a(b + c) = ab + ac$. This means multiply each term inside the parentheses by the factor outside. 3. **Apply the distributive property:** $$3 \cdot (5x - 8) = 3 \cdot 5x - 3 \cdot 8$$ 4. **Multiply each term:** $$= 15x - 24$$ 5. **Final answer:** $$3 \cdot (5x - 8) = 15x - 24$$