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 Now, we will combine the like terms. #### Combining the \(x\) terms: - Start with \(3x\) and subtract \(2x\): \[ 3x - 2x = (3 - 2)x = 1x = x \] #### Combining the constant terms: - Now, add the constants \(5\) and \(7\): \[ 5 + 7 = 12 \] ### Step 3: Write the Simplified Expression After combining the like terms, we can write the simplified expression: \[ x + 12 \] ### Conclusion The final simplified form of the expression \(3x + 5 - 2x + 7\) is \(x + 12\). ### Answer The correct option is **A. \(x + 12\)**. ### Explanation of Other Options Now, let's analyze the other options to understand why they are incorrect: - **Option B: \(5x + 12\)** - This option incorrectly suggests that the coefficient of \(x\) is \(5\). However, we found that the coefficient is actually \(1\) after combining \(3x\) and \(-2x\). - **Option C: \(x + 2\)** - This option incorrectly states that the constant term is \(2\). We calculated the constant terms to be \(12\), not \(2\). - **Option D: \(x + 6\)** - Similar to option C, this option incorrectly states that the constant term is \(6\). Our calculation showed that the correct constant term is \(12\). ### Common Pitfalls - **Forgetting to combine like terms**: Always ensure you group and combine terms that are similar (i.e., terms with the same variable or constant terms). - **Miscalculating constants**: Double-check your arithmetic when adding or subtracting constants to avoid errors. ### Revision Summary - Identify and group like terms in an expression. - Combine coefficients of \(x\) and constant terms separately. - Ensure to double-check calculations to avoid simple arithmetic mistakes. - The simplified form of \(3x + 5 - 2x + 7\) is \(x + 12\).