1. **State the problem:** Simplify fully the expression $3(2x - 5) - 4(x + 1)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$3(2x - 5) - 4(x + 1) = 3 \times 2x - 3 \times 5 - 4 \times x - 4 \times 1$$ 3. **Calculate each multiplication:** $$= 6x - 15 - 4x - 4$$ 4. **Combine like terms:** Group the $x$ terms and the constants. $$6x - 4x - 15 - 4$$ 5. **Simplify the expression:** $$= (6x - 4x) + (-15 - 4) = 2x - 19$$ **Final answer:** $$\boxed{2x - 19}$$