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Simplifying 30 + -1[1 + 8y + -2(y + 3)] = -4(3y + -5) + -1[9(y + -1) + -8y + 15] Reorder the terms: 30 + -1[1 + 8y + -2(3 + y)] = -4(3y + -5) + -1[9(y + -1) + -8y + 15] 30 + -1[1 + 8y + (3 * -2 + y * -2)] = -4(3y + -5) + -1[9(y + -1) + -8y + 15] 30 + -1[1 + 8y + (-6 + -2y)] = -4(3y + -5) + -1[9(y + -1) + -8y + 15] Reorder the terms: 30 + -1[1 + -6 + 8y + -2y] = -4(3y + -5) + -1[9(y + -1) + -8y + 15] Combine like terms: 1 + -6 = -5 30 + -1[-5 + 8y + -2y] = -4(3y + -5) + -1[9(y + -1) + -8y + 15] Combine like terms: 8y + -2y = 6y 30 + -1[-5 + 6y] = -4(3y + -5) + -1[9(y + -1) + -8y + 15] 30 + [-5 * -1 + 6y * -1] = -4(3y + -5) + -1[9(y + -1) + -8y + 15] 30 + [5 + -6y] = -4(3y + -5) + -1[9(y + -1) + -8y + 15] Combine like terms: 30 + 5 = 35 35 + -6y = -4(3y + -5) + -1[9(y + -1) + -8y + 15] Reorder the terms: 35 + -6y = -4(-5 + 3y) + -1[9(y + -1) + -8y + 15] 35 + -6y = (-5 * -4 + 3y * -4) + -1[9(y + -1) + -8y + 15] 35 + -6y = (20 + -12y) + -1[9(y + -1) + -8y + 15] Reorder the terms: 35 + -6y = 20 + -12y + -1[9(-1 + y) + -8y + 15] 35 + -6y = 20 + -12y + -1[(-1 * 9 + y * 9) + -8y + 15] 35 + -6y = 20 + -12y + -1[(-9 + 9y) + -8y + 15] Reorder the terms: 35 + -6y = 20 + -12y + -1[-9 + 15 + 9y + -8y] Combine like terms: -9 + 15 = 6 35 + -6y = 20 + -12y + -1[6 + 9y + -8y] Combine like terms: 9y + -8y = 1y 35 + -6y = 20 + -12y + -1[6 + 1y] 35 + -6y = 20 + -12y + [6 * -1 + 1y * -1] 35 + -6y = 20 + -12y + [-6 + -1y] Reorder the terms: 35 + -6y = 20 + -6 + -12y + -1y Combine like terms: 20 + -6 = 14 35 + -6y = 14 + -12y + -1y Combine like terms: -12y + -1y = -13y 35 + -6y = 14 + -13y Solving 35 + -6y = 14 + -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. 35 + -6y + 13y = 14 + -13y + 13y Combine like terms: -6y + 13y = 7y 35 + 7y = 14 + -13y + 13y Combine like terms: -13y + 13y = 0 35 + 7y = 14 + 0 35 + 7y = 14 Add '-35' to each side of the equation. 35 + -35 + 7y = 14 + -35 Combine like terms: 35 + -35 = 0 0 + 7y = 14 + -35 7y = 14 + -35 Combine like terms: 14 + -35 = -21 7y = -21 Divide each side by '7'. y = -3 Simplifying y = -3
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