1. Stating the problem: Simplify the algebraic expression $x + 2y + 4x - 3y$. 2. Formula and rules: Combine like terms by adding or subtracting coefficients of the same variables. 3. Intermediate work: - Combine $x$ terms: $x + 4x = 5x$ - Combine $y$ terms: $2y - 3y = -y$ 4. Final simplified expression: $$5x - y$$ This means the expression simplifies to $5x - y$ by grouping and combining like terms.