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Opposite of Sum and Difference Simplification

This guide simplifies equations involving the opposite of a sum or difference and provides examples for easy understanding.

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Opposite of Sum and Difference Simplification

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  1. Simplify the following. Objective - To find the opposite of a sum or difference. Opposite of a sum Opposite of a difference = -x + -y = -x + y -(x + y) -(x - y) -1(x + y) = -1x + -1y -1(x - y) = -1x + 1y

  2. Subtracting a Sum or Difference Judy has $10, owes Sam $3, and owes Talia $5. How much will she have after paying them? Distribute the negative!

  3. Subtracting a Quantity 1) -(x + 6) 6) -(3a + 1) -x - 6 -3a - 1 2) -(2x - 8) 7) -(-3x + 2y - 7) -2x + 16 +3x - 2y + 7 3) 10 - (4m + 3) 8) -12 - (3y - 8) 10 - 4m - 3 -12 - 3y + 8 - 4m + 7 - 3y - 4 4) 2(x - 5) - (x - 3) 9) 4(3k - 5) - (2k + 9) 2x - 10 - x + 3 12k - 20 - 2k - 9 x - 7 10k - 29

  4. Simplify the following. 1) 10 - 4(x - 5) - 8 4) 5x - 4(7x - 9) - 11 5x - 28x + 36 - 11 10 - 4x + 20 - 8 - 23x + 25 - 4x + 22 2) 6 -2(5 - x) - (3x + 7) 5) 10 + 3(x - 5) - (2x - 9) 10 + 3x - 15 - 2x + 18 6 - 10 + 2x - 3x - 7 x + 13 - x - 11 3) 4x - 5[2(6x - 3) - 7] 6) -4[-(x + 5) - 3(x - 6)] -4[-x + -5 - 3x + 18] 4x - 5[12x - 6 - 7] -4[-4x + 13] 4x - 5[12x - 13] 4x - 60x + 65 16x - 52 -56x + 65

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