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Simplifying 14 + -1[3 + 9y + -4(y + 4)] = -4(2y + -5) + -1[5(y + -1) + -6y + 12] Reorder the terms: 14 + -1[3 + 9y + -4(4 + y)] = -4(2y + -5) + -1[5(y + -1) + -6y + 12] 14 + -1[3 + 9y + (4 * -4 + y * -4)] = -4(2y + -5) + -1[5(y + -1) + -6y + 12] 14 + -1[3 + 9y + (-16 + -4y)] = -4(2y + -5) + -1[5(y + -1) + -6y + 12] Reorder the terms: 14 + -1[3 + -16 + 9y + -4y] = -4(2y + -5) + -1[5(y + -1) + -6y + 12] Combine like terms: 3 + -16 = -13 14 + -1[-13 + 9y + -4y] = -4(2y + -5) + -1[5(y + -1) + -6y + 12] Combine like terms: 9y + -4y = 5y 14 + -1[-13 + 5y] = -4(2y + -5) + -1[5(y + -1) + -6y + 12] 14 + [-13 * -1 + 5y * -1] = -4(2y + -5) + -1[5(y + -1) + -6y + 12] 14 + [13 + -5y] = -4(2y + -5) + -1[5(y + -1) + -6y + 12] Combine like terms: 14 + 13 = 27 27 + -5y = -4(2y + -5) + -1[5(y + -1) + -6y + 12] Reorder the terms: 27 + -5y = -4(-5 + 2y) + -1[5(y + -1) + -6y + 12] 27 + -5y = (-5 * -4 + 2y * -4) + -1[5(y + -1) + -6y + 12] 27 + -5y = (20 + -8y) + -1[5(y + -1) + -6y + 12] Reorder the terms: 27 + -5y = 20 + -8y + -1[5(-1 + y) + -6y + 12] 27 + -5y = 20 + -8y + -1[(-1 * 5 + y * 5) + -6y + 12] 27 + -5y = 20 + -8y + -1[(-5 + 5y) + -6y + 12] Reorder the terms: 27 + -5y = 20 + -8y + -1[-5 + 12 + 5y + -6y] Combine like terms: -5 + 12 = 7 27 + -5y = 20 + -8y + -1[7 + 5y + -6y] Combine like terms: 5y + -6y = -1y 27 + -5y = 20 + -8y + -1[7 + -1y] 27 + -5y = 20 + -8y + [7 * -1 + -1y * -1] 27 + -5y = 20 + -8y + [-7 + 1y] Reorder the terms: 27 + -5y = 20 + -7 + -8y + 1y Combine like terms: 20 + -7 = 13 27 + -5y = 13 + -8y + 1y Combine like terms: -8y + 1y = -7y 27 + -5y = 13 + -7y Solving 27 + -5y = 13 + -7y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7y' to each side of the equation. 27 + -5y + 7y = 13 + -7y + 7y Combine like terms: -5y + 7y = 2y 27 + 2y = 13 + -7y + 7y Combine like terms: -7y + 7y = 0 27 + 2y = 13 + 0 27 + 2y = 13 Add '-27' to each side of the equation. 27 + -27 + 2y = 13 + -27 Combine like terms: 27 + -27 = 0 0 + 2y = 13 + -27 2y = 13 + -27 Combine like terms: 13 + -27 = -14 2y = -14 Divide each side by '2'. y = -7 Simplifying y = -7
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