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Simplifying 27 + -1[5 + 6y + -3(y + 4)] = -3(2y + -4) + -1[8(y + -1) + -7y + 6] Reorder the terms: 27 + -1[5 + 6y + -3(4 + y)] = -3(2y + -4) + -1[8(y + -1) + -7y + 6] 27 + -1[5 + 6y + (4 * -3 + y * -3)] = -3(2y + -4) + -1[8(y + -1) + -7y + 6] 27 + -1[5 + 6y + (-12 + -3y)] = -3(2y + -4) + -1[8(y + -1) + -7y + 6] Reorder the terms: 27 + -1[5 + -12 + 6y + -3y] = -3(2y + -4) + -1[8(y + -1) + -7y + 6] Combine like terms: 5 + -12 = -7 27 + -1[-7 + 6y + -3y] = -3(2y + -4) + -1[8(y + -1) + -7y + 6] Combine like terms: 6y + -3y = 3y 27 + -1[-7 + 3y] = -3(2y + -4) + -1[8(y + -1) + -7y + 6] 27 + [-7 * -1 + 3y * -1] = -3(2y + -4) + -1[8(y + -1) + -7y + 6] 27 + [7 + -3y] = -3(2y + -4) + -1[8(y + -1) + -7y + 6] Combine like terms: 27 + 7 = 34 34 + -3y = -3(2y + -4) + -1[8(y + -1) + -7y + 6] Reorder the terms: 34 + -3y = -3(-4 + 2y) + -1[8(y + -1) + -7y + 6] 34 + -3y = (-4 * -3 + 2y * -3) + -1[8(y + -1) + -7y + 6] 34 + -3y = (12 + -6y) + -1[8(y + -1) + -7y + 6] Reorder the terms: 34 + -3y = 12 + -6y + -1[8(-1 + y) + -7y + 6] 34 + -3y = 12 + -6y + -1[(-1 * 8 + y * 8) + -7y + 6] 34 + -3y = 12 + -6y + -1[(-8 + 8y) + -7y + 6] Reorder the terms: 34 + -3y = 12 + -6y + -1[-8 + 6 + 8y + -7y] Combine like terms: -8 + 6 = -2 34 + -3y = 12 + -6y + -1[-2 + 8y + -7y] Combine like terms: 8y + -7y = 1y 34 + -3y = 12 + -6y + -1[-2 + 1y] 34 + -3y = 12 + -6y + [-2 * -1 + 1y * -1] 34 + -3y = 12 + -6y + [2 + -1y] Reorder the terms: 34 + -3y = 12 + 2 + -6y + -1y Combine like terms: 12 + 2 = 14 34 + -3y = 14 + -6y + -1y Combine like terms: -6y + -1y = -7y 34 + -3y = 14 + -7y Solving 34 + -3y = 14 + -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. 34 + -3y + 7y = 14 + -7y + 7y Combine like terms: -3y + 7y = 4y 34 + 4y = 14 + -7y + 7y Combine like terms: -7y + 7y = 0 34 + 4y = 14 + 0 34 + 4y = 14 Add '-34' to each side of the equation. 34 + -34 + 4y = 14 + -34 Combine like terms: 34 + -34 = 0 0 + 4y = 14 + -34 4y = 14 + -34 Combine like terms: 14 + -34 = -20 4y = -20 Divide each side by '4'. y = -5 Simplifying y = -5
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