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Simplifying 27 + -1[4 + 6y + -3(y + 5)] = -2(3y + -5) + -1[8(y + -1) + -6y + 5] Reorder the terms: 27 + -1[4 + 6y + -3(5 + y)] = -2(3y + -5) + -1[8(y + -1) + -6y + 5] 27 + -1[4 + 6y + (5 * -3 + y * -3)] = -2(3y + -5) + -1[8(y + -1) + -6y + 5] 27 + -1[4 + 6y + (-15 + -3y)] = -2(3y + -5) + -1[8(y + -1) + -6y + 5] Reorder the terms: 27 + -1[4 + -15 + 6y + -3y] = -2(3y + -5) + -1[8(y + -1) + -6y + 5] Combine like terms: 4 + -15 = -11 27 + -1[-11 + 6y + -3y] = -2(3y + -5) + -1[8(y + -1) + -6y + 5] Combine like terms: 6y + -3y = 3y 27 + -1[-11 + 3y] = -2(3y + -5) + -1[8(y + -1) + -6y + 5] 27 + [-11 * -1 + 3y * -1] = -2(3y + -5) + -1[8(y + -1) + -6y + 5] 27 + [11 + -3y] = -2(3y + -5) + -1[8(y + -1) + -6y + 5] Combine like terms: 27 + 11 = 38 38 + -3y = -2(3y + -5) + -1[8(y + -1) + -6y + 5] Reorder the terms: 38 + -3y = -2(-5 + 3y) + -1[8(y + -1) + -6y + 5] 38 + -3y = (-5 * -2 + 3y * -2) + -1[8(y + -1) + -6y + 5] 38 + -3y = (10 + -6y) + -1[8(y + -1) + -6y + 5] Reorder the terms: 38 + -3y = 10 + -6y + -1[8(-1 + y) + -6y + 5] 38 + -3y = 10 + -6y + -1[(-1 * 8 + y * 8) + -6y + 5] 38 + -3y = 10 + -6y + -1[(-8 + 8y) + -6y + 5] Reorder the terms: 38 + -3y = 10 + -6y + -1[-8 + 5 + 8y + -6y] Combine like terms: -8 + 5 = -3 38 + -3y = 10 + -6y + -1[-3 + 8y + -6y] Combine like terms: 8y + -6y = 2y 38 + -3y = 10 + -6y + -1[-3 + 2y] 38 + -3y = 10 + -6y + [-3 * -1 + 2y * -1] 38 + -3y = 10 + -6y + [3 + -2y] Reorder the terms: 38 + -3y = 10 + 3 + -6y + -2y Combine like terms: 10 + 3 = 13 38 + -3y = 13 + -6y + -2y Combine like terms: -6y + -2y = -8y 38 + -3y = 13 + -8y Solving 38 + -3y = 13 + -8y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8y' to each side of the equation. 38 + -3y + 8y = 13 + -8y + 8y Combine like terms: -3y + 8y = 5y 38 + 5y = 13 + -8y + 8y Combine like terms: -8y + 8y = 0 38 + 5y = 13 + 0 38 + 5y = 13 Add '-38' to each side of the equation. 38 + -38 + 5y = 13 + -38 Combine like terms: 38 + -38 = 0 0 + 5y = 13 + -38 5y = 13 + -38 Combine like terms: 13 + -38 = -25 5y = -25 Divide each side by '5'. y = -5 Simplifying y = -5
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