1. **State the problem:** Simplify the expression $4x + 7x - 2y + 5y$. 2. **Formula and rules:** To simplify algebraic expressions, combine like terms. Like terms have the same variable raised to the same power. 3. **Combine like terms:** - Combine $4x$ and $7x$: $$4x + 7x = (4 + 7)x = 11x$$ - Combine $-2y$ and $5y$: $$-2y + 5y = (-2 + 5)y = 3y$$ 4. **Write the simplified expression:** $$11x + 3y$$ 5. **Explanation:** We grouped terms with $x$ and terms with $y$ separately and added their coefficients to simplify the expression. **Final answer:** $$11x + 3y$$