1. **State the problem:** Simplify the expression $4(x-3)-3(x-5)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$4(x-3)-3(x-5) = 4x - 12 - 3x + 15$$ 3. **Combine like terms:** Group the $x$ terms and the constant terms. $$4x - 3x - 12 + 15$$ 4. **Simplify:** $$\cancel{4x} - \cancel{3x} = x$$ $$-12 + 15 = 3$$ 5. **Final simplified expression:** $$x + 3$$ This means the original expression simplifies to $x + 3$.