1. **State the problem:** Simplify the expression $4x + 7(4 + y) - 3x$. 2. **Apply the distributive property:** Multiply 7 by each term inside the parentheses: $$7(4 + y) = 7 \times 4 + 7 \times y = 28 + 7y$$ 3. **Rewrite the expression:** $$4x + 28 + 7y - 3x$$ 4. **Combine like terms:** Combine $4x$ and $-3x$: $$4x - 3x = \cancel{4x}^1 - \cancel{3x}^1 = 1x = x$$ 5. **Final simplified expression:** $$x + 28 + 7y$$ This is the simplified form of the original expression.