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Simplifying 42 + -1[1 + 9y + -3(y + 3)] = -3(2y + -4) + -1[8(y + -1) + -1y + 5] Reorder the terms: 42 + -1[1 + 9y + -3(3 + y)] = -3(2y + -4) + -1[8(y + -1) + -1y + 5] 42 + -1[1 + 9y + (3 * -3 + y * -3)] = -3(2y + -4) + -1[8(y + -1) + -1y + 5] 42 + -1[1 + 9y + (-9 + -3y)] = -3(2y + -4) + -1[8(y + -1) + -1y + 5] Reorder the terms: 42 + -1[1 + -9 + 9y + -3y] = -3(2y + -4) + -1[8(y + -1) + -1y + 5] Combine like terms: 1 + -9 = -8 42 + -1[-8 + 9y + -3y] = -3(2y + -4) + -1[8(y + -1) + -1y + 5] Combine like terms: 9y + -3y = 6y 42 + -1[-8 + 6y] = -3(2y + -4) + -1[8(y + -1) + -1y + 5] 42 + [-8 * -1 + 6y * -1] = -3(2y + -4) + -1[8(y + -1) + -1y + 5] 42 + [8 + -6y] = -3(2y + -4) + -1[8(y + -1) + -1y + 5] Combine like terms: 42 + 8 = 50 50 + -6y = -3(2y + -4) + -1[8(y + -1) + -1y + 5] Reorder the terms: 50 + -6y = -3(-4 + 2y) + -1[8(y + -1) + -1y + 5] 50 + -6y = (-4 * -3 + 2y * -3) + -1[8(y + -1) + -1y + 5] 50 + -6y = (12 + -6y) + -1[8(y + -1) + -1y + 5] Reorder the terms: 50 + -6y = 12 + -6y + -1[8(-1 + y) + -1y + 5] 50 + -6y = 12 + -6y + -1[(-1 * 8 + y * 8) + -1y + 5] 50 + -6y = 12 + -6y + -1[(-8 + 8y) + -1y + 5] Reorder the terms: 50 + -6y = 12 + -6y + -1[-8 + 5 + 8y + -1y] Combine like terms: -8 + 5 = -3 50 + -6y = 12 + -6y + -1[-3 + 8y + -1y] Combine like terms: 8y + -1y = 7y 50 + -6y = 12 + -6y + -1[-3 + 7y] 50 + -6y = 12 + -6y + [-3 * -1 + 7y * -1] 50 + -6y = 12 + -6y + [3 + -7y] Reorder the terms: 50 + -6y = 12 + 3 + -6y + -7y Combine like terms: 12 + 3 = 15 50 + -6y = 15 + -6y + -7y Combine like terms: -6y + -7y = -13y 50 + -6y = 15 + -13y Solving 50 + -6y = 15 + -13y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '13y' to each side of the equation. 50 + -6y + 13y = 15 + -13y + 13y Combine like terms: -6y + 13y = 7y 50 + 7y = 15 + -13y + 13y Combine like terms: -13y + 13y = 0 50 + 7y = 15 + 0 50 + 7y = 15 Add '-50' to each side of the equation. 50 + -50 + 7y = 15 + -50 Combine like terms: 50 + -50 = 0 0 + 7y = 15 + -50 7y = 15 + -50 Combine like terms: 15 + -50 = -35 7y = -35 Divide each side by '7'. y = -5 Simplifying y = -5
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