To simplify the expression \(3(x + 4) - 2(x - 1)\), we will follow a step-by-step approach. ### Step 1: Distribute the coefficients First, we need to distribute the numbers outside the parentheses to the terms inside the parentheses. 1. For the first part, \(3(x + 4)\): - Multiply \(3\) by \(x\): \(3 \cdot x = 3x\) - Multiply \(3\) by \(4\): \(3 \cdot 4 = 12\) - So, \(3(x + 4) = 3x + 12\) 2. For the second part, \(-2(x - 1)\): - Multiply \(-2\) by \(x\): \(-2 \cdot x = -2x\) - Multiply \(-2\) by \(-1\): \(-2 \cdot -1 = 2\) (Note that multiplying two negatives gives a positive) - So, \(-2(x - 1) = -2x + 2\) ### Step 2: Combine the results Now we can combine the results from both distributions: \[ 3(x + 4) - 2(x - 1) = (3x + 12) + (-2x + 2) \] ### Step 3: Combine like terms Next, we will combine the like terms (the terms that contain \(x\) and the constant terms): 1. Combine the \(x\) terms: - \(3x - 2x = 1x\) or simply \(x\) 2. Combine the constant terms: - \(12 + 2 = 14\) Putting it all together, we have: \[ x + 14 \] ### Final Result Thus, the simplified expression is: \[ x + 14 \] ### Correct Option The correct option is **A. \(x + 14\)**. ### Explanation of Other Options - **Option B: \(x + 10\)**: This is incorrect because it does not account for the correct addition of the constant terms. The correct sum of the constants is \(12 + 2 = 14\), not \(10\). - **Option C: \(x + 8\)**: This is also incorrect. It suggests that the constant terms add up to \(8\), which is not the case. The correct addition is \(14\). - **Option D: \(x + 12\)**: This option is incorrect as well. It implies that the constant term is \(12\), which only accounts for the first part of the expression and ignores the contribution from the second part. ### Summary of Key Points - Distribute coefficients correctly to terms inside parentheses. - Combine like terms carefully, ensuring to add both \(x\) terms and constant terms. - Always double-check your arithmetic when combining constants. - The final simplified expression for \(3(x + 4) - 2(x - 1)\) is \(x + 14\).