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Simplifying 21 + -1[2 + 8y + -3(y + 4)] = -3(2y + -5) + -1[9(y + -1) + -7y + 11] Reorder the terms: 21 + -1[2 + 8y + -3(4 + y)] = -3(2y + -5) + -1[9(y + -1) + -7y + 11] 21 + -1[2 + 8y + (4 * -3 + y * -3)] = -3(2y + -5) + -1[9(y + -1) + -7y + 11] 21 + -1[2 + 8y + (-12 + -3y)] = -3(2y + -5) + -1[9(y + -1) + -7y + 11] Reorder the terms: 21 + -1[2 + -12 + 8y + -3y] = -3(2y + -5) + -1[9(y + -1) + -7y + 11] Combine like terms: 2 + -12 = -10 21 + -1[-10 + 8y + -3y] = -3(2y + -5) + -1[9(y + -1) + -7y + 11] Combine like terms: 8y + -3y = 5y 21 + -1[-10 + 5y] = -3(2y + -5) + -1[9(y + -1) + -7y + 11] 21 + [-10 * -1 + 5y * -1] = -3(2y + -5) + -1[9(y + -1) + -7y + 11] 21 + [10 + -5y] = -3(2y + -5) + -1[9(y + -1) + -7y + 11] Combine like terms: 21 + 10 = 31 31 + -5y = -3(2y + -5) + -1[9(y + -1) + -7y + 11] Reorder the terms: 31 + -5y = -3(-5 + 2y) + -1[9(y + -1) + -7y + 11] 31 + -5y = (-5 * -3 + 2y * -3) + -1[9(y + -1) + -7y + 11] 31 + -5y = (15 + -6y) + -1[9(y + -1) + -7y + 11] Reorder the terms: 31 + -5y = 15 + -6y + -1[9(-1 + y) + -7y + 11] 31 + -5y = 15 + -6y + -1[(-1 * 9 + y * 9) + -7y + 11] 31 + -5y = 15 + -6y + -1[(-9 + 9y) + -7y + 11] Reorder the terms: 31 + -5y = 15 + -6y + -1[-9 + 11 + 9y + -7y] Combine like terms: -9 + 11 = 2 31 + -5y = 15 + -6y + -1[2 + 9y + -7y] Combine like terms: 9y + -7y = 2y 31 + -5y = 15 + -6y + -1[2 + 2y] 31 + -5y = 15 + -6y + [2 * -1 + 2y * -1] 31 + -5y = 15 + -6y + [-2 + -2y] Reorder the terms: 31 + -5y = 15 + -2 + -6y + -2y Combine like terms: 15 + -2 = 13 31 + -5y = 13 + -6y + -2y Combine like terms: -6y + -2y = -8y 31 + -5y = 13 + -8y Solving 31 + -5y = 13 + -8y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8y' to each side of the equation. 31 + -5y + 8y = 13 + -8y + 8y Combine like terms: -5y + 8y = 3y 31 + 3y = 13 + -8y + 8y Combine like terms: -8y + 8y = 0 31 + 3y = 13 + 0 31 + 3y = 13 Add '-31' to each side of the equation. 31 + -31 + 3y = 13 + -31 Combine like terms: 31 + -31 = 0 0 + 3y = 13 + -31 3y = 13 + -31 Combine like terms: 13 + -31 = -18 3y = -18 Divide each side by '3'. y = -6 Simplifying y = -6
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