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 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 with \( x \) 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: \[ -x + 14 \] ### Final Result Thus, the simplified expression is: \[ -x + 14 \] ### Answer Selection Now, let's look at the options provided: - A. \( x + 14 \) - B. \( -x + 10 \) - C. \( 7 - x \) - D. \( 5x + 10 \) The correct answer is not listed among the options provided. The correct simplified expression is \( -x + 14 \), which is not present in the options. ### Explanation of Incorrect Options - **Option A: \( x + 14 \)** - This is incorrect because it has the wrong sign for the \( x \) term. The correct term is \( -x \), not \( x \). - **Option B: \( -x + 10 \)** - This is incorrect because, while it has the correct sign for the \( x \) term, the constant term is wrong. The correct constant term is \( 14 \), not \( 10 \). - **Option C: \( 7 - x \)** - This is incorrect because it has the wrong constant term. The correct constant term is \( 14 \), not \( 7 \). - **Option D: \( 5x + 10 \)** - This is incorrect because it has the wrong coefficients for the \( x \) term and the wrong constant term. The correct expression does not have a positive \( 5x \) term. ### Revision Summary - To simplify expressions, distribute coefficients to terms inside parentheses. - Combine like terms carefully, ensuring to keep track of signs. - Always double-check your final expression against the provided options. - If the correct answer is not among the options, verify your calculations for accuracy. In this case, the correct simplified expression is \( -x + 14 \).