To simplify the expression \( 3(2x + 4) - 5(x - 2) \), we will follow a step-by-step approach. ### Step 1: Distribute the constants First, we need to distribute the constants outside the parentheses to the terms inside the parentheses. 1. For the first part, \( 3(2x + 4) \): - Multiply \( 3 \) by \( 2x \): \[ 3 \times 2x = 6x \] - Multiply \( 3 \) by \( 4 \): \[ 3 \times 4 = 12 \] - So, \( 3(2x + 4) = 6x + 12 \). 2. For the second part, \( -5(x - 2) \): - Multiply \( -5 \) by \( x \): \[ -5 \times x = -5x \] - Multiply \( -5 \) by \( -2 \): \[ -5 \times -2 = 10 \] - So, \( -5(x - 2) = -5x + 10 \). ### Step 2: Combine the results Now we can combine the results from both distributions: \[ 6x + 12 - 5x + 10 \] ### 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: \[ 6x - 5x = 1x \quad \text{(or simply } x\text{)} \] 2. Combine the constant terms: \[ 12 + 10 = 22 \] ### Final Result Putting it all together, we have: \[ x + 22 \] ### Conclusion The simplified expression is \( x + 22 \). ### Answer The correct option is **B. \( x + 22 \)**. ### Explanation of Other Options - **Option A**: [blank] - This option does not provide any expression, so it cannot be correct. - **Option C**: [blank] - Similar to Option A, this option is also blank and cannot be correct. - **Option D**: \( x + 10 \) - This option is incorrect because we correctly calculated the constant term to be \( 22 \), not \( 10 \). ### Revision Summary - Distribute constants to terms inside parentheses carefully. - Combine like terms (both variable and constant terms) after distribution. - Always double-check calculations to avoid simple arithmetic errors. - The final simplified expression for \( 3(2x + 4) - 5(x - 2) \) is \( x + 22 \).