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Simplifying 29 + -1[5 + 7y + -2(y + 2)] = -5(5y + -6) + -1[8(y + -1) + -21y + 24] Reorder the terms: 29 + -1[5 + 7y + -2(2 + y)] = -5(5y + -6) + -1[8(y + -1) + -21y + 24] 29 + -1[5 + 7y + (2 * -2 + y * -2)] = -5(5y + -6) + -1[8(y + -1) + -21y + 24] 29 + -1[5 + 7y + (-4 + -2y)] = -5(5y + -6) + -1[8(y + -1) + -21y + 24] Reorder the terms: 29 + -1[5 + -4 + 7y + -2y] = -5(5y + -6) + -1[8(y + -1) + -21y + 24] Combine like terms: 5 + -4 = 1 29 + -1[1 + 7y + -2y] = -5(5y + -6) + -1[8(y + -1) + -21y + 24] Combine like terms: 7y + -2y = 5y 29 + -1[1 + 5y] = -5(5y + -6) + -1[8(y + -1) + -21y + 24] 29 + [1 * -1 + 5y * -1] = -5(5y + -6) + -1[8(y + -1) + -21y + 24] 29 + [-1 + -5y] = -5(5y + -6) + -1[8(y + -1) + -21y + 24] Combine like terms: 29 + -1 = 28 28 + -5y = -5(5y + -6) + -1[8(y + -1) + -21y + 24] Reorder the terms: 28 + -5y = -5(-6 + 5y) + -1[8(y + -1) + -21y + 24] 28 + -5y = (-6 * -5 + 5y * -5) + -1[8(y + -1) + -21y + 24] 28 + -5y = (30 + -25y) + -1[8(y + -1) + -21y + 24] Reorder the terms: 28 + -5y = 30 + -25y + -1[8(-1 + y) + -21y + 24] 28 + -5y = 30 + -25y + -1[(-1 * 8 + y * 8) + -21y + 24] 28 + -5y = 30 + -25y + -1[(-8 + 8y) + -21y + 24] Reorder the terms: 28 + -5y = 30 + -25y + -1[-8 + 24 + 8y + -21y] Combine like terms: -8 + 24 = 16 28 + -5y = 30 + -25y + -1[16 + 8y + -21y] Combine like terms: 8y + -21y = -13y 28 + -5y = 30 + -25y + -1[16 + -13y] 28 + -5y = 30 + -25y + [16 * -1 + -13y * -1] 28 + -5y = 30 + -25y + [-16 + 13y] Reorder the terms: 28 + -5y = 30 + -16 + -25y + 13y Combine like terms: 30 + -16 = 14 28 + -5y = 14 + -25y + 13y Combine like terms: -25y + 13y = -12y 28 + -5y = 14 + -12y Solving 28 + -5y = 14 + -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. 28 + -5y + 12y = 14 + -12y + 12y Combine like terms: -5y + 12y = 7y 28 + 7y = 14 + -12y + 12y Combine like terms: -12y + 12y = 0 28 + 7y = 14 + 0 28 + 7y = 14 Add '-28' to each side of the equation. 28 + -28 + 7y = 14 + -28 Combine like terms: 28 + -28 = 0 0 + 7y = 14 + -28 7y = 14 + -28 Combine like terms: 14 + -28 = -14 7y = -14 Divide each side by '7'. y = -2 Simplifying y = -2
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