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Which expression is equivalent to 2(4x+7)-3(8x-4) ? (A) -16x+2 (B) -16x+26 (C) -20x+22 (D) 8x

Which expression is equivalent to 2(4x+7)−3(8x−4) 2(4 x+7)-3(8 x-4) ?\newline(A) −16x+2 -16x+2 \newline(B) −16x+26 -16x+26 \newline(C) −20x+22 -20x+22 \newline(D) 8x 8 x

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Q. Which expression is equivalent to 2(4x+7)−3(8x−4) 2(4 x+7)-3(8 x-4) ?\newline(A) −16x+2 -16x+2 \newline(B) −16x+26 -16x+26 \newline(C) −20x+22 -20x+22 \newline(D) 8x 8 x
  1. Distribute 22 into terms: Distribute the 22 into the terms inside the first parentheses.2(4x+7)2(4x+7) becomes 2⋅4x+2⋅72\cdot4x + 2\cdot7. Calculation: 2⋅4x=8x2\cdot4x = 8x and 2⋅7=142\cdot7 = 14. So, 2(4x+7)=8x+142(4x+7) = 8x + 14.
  2. Distribute −3-3 into terms: Distribute the −3-3 into the terms inside the second parentheses.−3(8x−4)-3(8x-4) becomes −3×8x+−3×(−4)-3\times 8x + -3\times (-4). Calculation: −3×8x=−24x-3\times 8x = -24x and −3×(−4)=12-3\times (-4) = 12. So, −3(8x−4)=−24x+12-3(8x-4) = -24x + 12.
  3. Combine distributed results: Combine the results from Step 11 and Step 22.\newlineWe have 8x+148x + 14 from the first expression and −24x+12-24x + 12 from the second expression.\newlineCombining them gives us (8x+14)+(−24x+12)(8x + 14) + (-24x + 12).
  4. Combine like terms: Combine like terms.\newline8x+(−24x)8x + (-24x) gives us −16x-16x.\newline14+1214 + 12 gives us 2626.\newlineSo, the combined expression is −16x+26-16x + 26.

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