To simplify the expression \(3x + 5y - 2x + 4\), we will follow a step-by-step approach to combine like terms. ### Step-by-Step Explanation 1. **Identify Like Terms**: - In the expression \(3x + 5y - 2x + 4\), we can identify the like terms: - The terms involving \(x\) are \(3x\) and \(-2x\). - The term involving \(y\) is \(5y\). - The constant term is \(4\). 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: \[ 5y \] - Finally, the constant term is: \[ 4 \] 3. **Write the Simplified Expression**: - Now, we can combine all the simplified parts together: \[ x + 5y + 4 \] ### Final Result The resulting expression after simplification is: \[ x + 5y + 4 \] ### Correct Option Thus, the correct option is **A. \(x + 5y + 4\)**. ### Explanation of Other Options - **Option B: \(x + 5y - 4\)**: This option incorrectly has a negative sign before the constant term. The constant term in our simplified expression is \(+4\), not \(-4\). - **Option C: \(5y + 4\)**: This option omits the \(x\) term entirely. While it correctly includes \(5y\) and \(4\), it fails to account for the \(x\) term, which is essential in the original expression. - **Option D: \(x + 4\)**: This option also omits the \(y\) term. It includes the \(x\) term and the constant \(4\), but it does not include \(5y\), which is a crucial part of the original expression. ### Common Pitfalls - **Forgetting to Combine Like Terms**: A common mistake is to overlook combining terms that are similar, such as \(3x\) and \(-2x\). - **Misplacing Signs**: Be careful with the signs of the terms, especially when subtracting. Ensure that you correctly apply the negative sign to the term being subtracted. ### Revision Summary - To simplify an expression, identify and combine like terms. - Carefully handle the signs of each term during simplification. - Ensure that all terms from the original expression are included in the final result. - The correct simplified expression for \(3x + 5y - 2x + 4\) is \(x + 5y + 4\).