To simplify the expression \(3x + 4y - 2x + 5\), we will follow a step-by-step approach to combine like terms and arrive at the simplest form. ### Step-by-Step Explanation 1. **Identify Like Terms**: - In the expression \(3x + 4y - 2x + 5\), we can identify the like terms: - The terms involving \(x\) are \(3x\) and \(-2x\). - The term involving \(y\) is \(4y\). - The constant term is \(5\). 2. **Combine the Like Terms**: - Start with the \(x\) terms: \[ 3x - 2x = (3 - 2)x = 1x = x \] - Next, we have the \(y\) term, which remains unchanged: \[ 4y \] - Finally, the constant term is: \[ 5 \] 3. **Write the Simplified Expression**: - Now, we can combine all the simplified parts: \[ x + 4y + 5 \] Thus, the expression \(3x + 4y - 2x + 5\) simplifies to \(x + 4y + 5\). ### Conclusion The correct option that represents the expression in its simplest form is **A. \(x + 4y + 5\)**. ### Explanation of Other Options - **Option B: \(x + 4y - 5\)**: This option incorrectly subtracts \(5\) instead of keeping it positive. The constant term in the original expression is \(+5\), not \(-5\). - **Option C: \(x + 4y + 7\)**: This option incorrectly adds \(2\) to the constant term. The original constant term is \(5\), so it should not be \(7\). - **Option D: \(5y + 5\)**: This option incorrectly changes the coefficient of \(y\) from \(4\) to \(5\) and omits the \(x\) term entirely. The original expression contains \(4y\), not \(5y\). ### Common Pitfalls - **Forgetting to combine like terms**: Always ensure that you only combine terms that have the same variable. - **Mismanaging signs**: Pay close attention to the signs in front of each term, especially when subtracting terms. ### Revision Summary - To simplify an expression, identify and combine like terms. - Carefully manage the signs of each term during simplification. - The final expression should include all variables and constants correctly combined. - Always double-check your work to avoid common mistakes in arithmetic and sign management.