1. State the problem: Simplify fully the expression $3(2x - 5) - 4(x + 1)$.\n\n2. Apply the distributive property: Multiply each term inside the parentheses by the factor outside.\n$$3(2x - 5) - 4(x + 1) = 3 \times 2x - 3 \times 5 - 4 \times x - 4 \times 1$$\n\n3. Calculate each multiplication:\n$$= 6x - 15 - 4x - 4$$\n\n4. Combine like terms: group the $x$ terms and the constants.\n$$= (6x - 4x) + (-15 - 4)$$\n\n5. Simplify each group:\n$$= 2x - 19$$\n\nFinal answer: $$2x - 19$$