To simplify the expression \( 3(x + 4) - 2(2x - 1) \), we will follow a step-by-step approach. ### Step 1: Distribute the coefficients First, we need to distribute the coefficients (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, \( -2(2x - 1) \): - Multiply \( -2 \) by \( 2x \): \( -2 \cdot 2x = -4x \) - Multiply \( -2 \) by \( -1 \): \( -2 \cdot -1 = 2 \) - So, \( -2(2x - 1) = -4x + 2 \) ### Step 2: Combine the results Now we can combine the results from both distributions: \[ 3(x + 4) - 2(2x - 1) = (3x + 12) + (-4x + 2) \] This simplifies to: \[ 3x + 12 - 4x + 2 \] ### 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: - \( 3x - 4x = -1x \) or simply \( -x \) 2. Combine the constant terms: - \( 12 + 2 = 14 \) Putting it all together, we have: \[ -x + 14 \] ### Step 4: Rewrite the expression We can rewrite \( -x + 14 \) as: \[ 14 - x \] ### Final Answer The simplified expression is \( 14 - x \). However, since the options provided do not include this form, we need to check if we can express it in a way that matches one of the options. ### Evaluating the Options Now, let's evaluate the options given: - **A. \( x + 14 \)**: This is incorrect because it suggests that \( x \) is positive and added to 14, which is not the case. - **B. \( x + 10 \)**: This is incorrect because it does not match our simplified expression. - **C. \( x + 5 \)**: This is incorrect for the same reason as above. - **D. \( x + 11 \)**: This is also incorrect. ### Conclusion None of the options provided match the correct simplified expression \( 14 - x \). Therefore, the correct answer is not listed among the options. ### Revision Summary - Distribute coefficients to terms inside parentheses. - Combine like terms carefully. - Always check if the final expression matches the options provided. - If the expression does not match any options, re-evaluate the simplification process. In this case, the correct simplified expression is \( 14 - x \), which does not correspond to any of the provided options.