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Simplifying 32 + -1[5 + 8y + -2(y + 2)] = -5(4y + -4) + -1[8(y + -1) + -16y + 15] Reorder the terms: 32 + -1[5 + 8y + -2(2 + y)] = -5(4y + -4) + -1[8(y + -1) + -16y + 15] 32 + -1[5 + 8y + (2 * -2 + y * -2)] = -5(4y + -4) + -1[8(y + -1) + -16y + 15] 32 + -1[5 + 8y + (-4 + -2y)] = -5(4y + -4) + -1[8(y + -1) + -16y + 15] Reorder the terms: 32 + -1[5 + -4 + 8y + -2y] = -5(4y + -4) + -1[8(y + -1) + -16y + 15] Combine like terms: 5 + -4 = 1 32 + -1[1 + 8y + -2y] = -5(4y + -4) + -1[8(y + -1) + -16y + 15] Combine like terms: 8y + -2y = 6y 32 + -1[1 + 6y] = -5(4y + -4) + -1[8(y + -1) + -16y + 15] 32 + [1 * -1 + 6y * -1] = -5(4y + -4) + -1[8(y + -1) + -16y + 15] 32 + [-1 + -6y] = -5(4y + -4) + -1[8(y + -1) + -16y + 15] Combine like terms: 32 + -1 = 31 31 + -6y = -5(4y + -4) + -1[8(y + -1) + -16y + 15] Reorder the terms: 31 + -6y = -5(-4 + 4y) + -1[8(y + -1) + -16y + 15] 31 + -6y = (-4 * -5 + 4y * -5) + -1[8(y + -1) + -16y + 15] 31 + -6y = (20 + -20y) + -1[8(y + -1) + -16y + 15] Reorder the terms: 31 + -6y = 20 + -20y + -1[8(-1 + y) + -16y + 15] 31 + -6y = 20 + -20y + -1[(-1 * 8 + y * 8) + -16y + 15] 31 + -6y = 20 + -20y + -1[(-8 + 8y) + -16y + 15] Reorder the terms: 31 + -6y = 20 + -20y + -1[-8 + 15 + 8y + -16y] Combine like terms: -8 + 15 = 7 31 + -6y = 20 + -20y + -1[7 + 8y + -16y] Combine like terms: 8y + -16y = -8y 31 + -6y = 20 + -20y + -1[7 + -8y] 31 + -6y = 20 + -20y + [7 * -1 + -8y * -1] 31 + -6y = 20 + -20y + [-7 + 8y] Reorder the terms: 31 + -6y = 20 + -7 + -20y + 8y Combine like terms: 20 + -7 = 13 31 + -6y = 13 + -20y + 8y Combine like terms: -20y + 8y = -12y 31 + -6y = 13 + -12y Solving 31 + -6y = 13 + -12y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12y' to each side of the equation. 31 + -6y + 12y = 13 + -12y + 12y Combine like terms: -6y + 12y = 6y 31 + 6y = 13 + -12y + 12y Combine like terms: -12y + 12y = 0 31 + 6y = 13 + 0 31 + 6y = 13 Add '-31' to each side of the equation. 31 + -31 + 6y = 13 + -31 Combine like terms: 31 + -31 = 0 0 + 6y = 13 + -31 6y = 13 + -31 Combine like terms: 13 + -31 = -18 6y = -18 Divide each side by '6'. y = -3 Simplifying y = -3
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