To simplify the expression \( 3x + 5 - 2x + 7 \), we will follow a systematic approach. Let's break it down step-by-step. ### Step 1: Identify Like Terms In the expression \( 3x + 5 - 2x + 7 \), we can identify two types of terms: - **Like terms involving \( x \)**: \( 3x \) and \( -2x \) - **Constant terms**: \( 5 \) and \( 7 \) ### Step 2: Combine Like Terms We will first combine the like terms involving \( x \): - Start with \( 3x \) and subtract \( 2x \): \[ 3x - 2x = (3 - 2)x = 1x = x \] Next, we combine the constant terms: - Add \( 5 \) and \( 7 \): \[ 5 + 7 = 12 \] ### Step 3: Write the Simplified Expression Now that we have combined both types of terms, we can write the simplified expression: \[ x + 12 \] ### Conclusion The final simplified expression is \( x + 12 \). ### Answer The correct option is **A. \( x + 12 \)**. ### Explanation of Other Options - **Option B: \( x + 2 \)**: This option is incorrect because it miscalculates the sum of the constant terms. The correct sum is \( 12 \), not \( 2 \). - **Option C: \( 5x + 12 \)**: This option incorrectly combines the \( x \) terms. The correct combination of \( 3x \) and \( -2x \) results in \( x \), not \( 5x \). - **Option D: \( 5x + 2 \)**: Similar to option C, this option also incorrectly combines the \( x \) terms and miscalculates the constant terms. The correct constant sum is \( 12 \), not \( 2 \). ### Common Pitfalls - **Forgetting to combine like terms**: Always ensure you group and combine like terms correctly. - **Misadding constants**: Double-check your arithmetic when adding or subtracting constant terms. ### Revision Summary - Identify and group like terms in the expression. - Combine the coefficients of \( x \) and the constant terms separately. - Ensure that all arithmetic is performed correctly to avoid mistakes. - The simplified expression for \( 3x + 5 - 2x + 7 \) is \( x + 12 \).