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Simplifying 21 + -1[2 + 6y + -2(y + 5)] = -4(2y + -3) + -1[9(y + -1) + -4y + 10] Reorder the terms: 21 + -1[2 + 6y + -2(5 + y)] = -4(2y + -3) + -1[9(y + -1) + -4y + 10] 21 + -1[2 + 6y + (5 * -2 + y * -2)] = -4(2y + -3) + -1[9(y + -1) + -4y + 10] 21 + -1[2 + 6y + (-10 + -2y)] = -4(2y + -3) + -1[9(y + -1) + -4y + 10] Reorder the terms: 21 + -1[2 + -10 + 6y + -2y] = -4(2y + -3) + -1[9(y + -1) + -4y + 10] Combine like terms: 2 + -10 = -8 21 + -1[-8 + 6y + -2y] = -4(2y + -3) + -1[9(y + -1) + -4y + 10] Combine like terms: 6y + -2y = 4y 21 + -1[-8 + 4y] = -4(2y + -3) + -1[9(y + -1) + -4y + 10] 21 + [-8 * -1 + 4y * -1] = -4(2y + -3) + -1[9(y + -1) + -4y + 10] 21 + [8 + -4y] = -4(2y + -3) + -1[9(y + -1) + -4y + 10] Combine like terms: 21 + 8 = 29 29 + -4y = -4(2y + -3) + -1[9(y + -1) + -4y + 10] Reorder the terms: 29 + -4y = -4(-3 + 2y) + -1[9(y + -1) + -4y + 10] 29 + -4y = (-3 * -4 + 2y * -4) + -1[9(y + -1) + -4y + 10] 29 + -4y = (12 + -8y) + -1[9(y + -1) + -4y + 10] Reorder the terms: 29 + -4y = 12 + -8y + -1[9(-1 + y) + -4y + 10] 29 + -4y = 12 + -8y + -1[(-1 * 9 + y * 9) + -4y + 10] 29 + -4y = 12 + -8y + -1[(-9 + 9y) + -4y + 10] Reorder the terms: 29 + -4y = 12 + -8y + -1[-9 + 10 + 9y + -4y] Combine like terms: -9 + 10 = 1 29 + -4y = 12 + -8y + -1[1 + 9y + -4y] Combine like terms: 9y + -4y = 5y 29 + -4y = 12 + -8y + -1[1 + 5y] 29 + -4y = 12 + -8y + [1 * -1 + 5y * -1] 29 + -4y = 12 + -8y + [-1 + -5y] Reorder the terms: 29 + -4y = 12 + -1 + -8y + -5y Combine like terms: 12 + -1 = 11 29 + -4y = 11 + -8y + -5y Combine like terms: -8y + -5y = -13y 29 + -4y = 11 + -13y Solving 29 + -4y = 11 + -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. 29 + -4y + 13y = 11 + -13y + 13y Combine like terms: -4y + 13y = 9y 29 + 9y = 11 + -13y + 13y Combine like terms: -13y + 13y = 0 29 + 9y = 11 + 0 29 + 9y = 11 Add '-29' to each side of the equation. 29 + -29 + 9y = 11 + -29 Combine like terms: 29 + -29 = 0 0 + 9y = 11 + -29 9y = 11 + -29 Combine like terms: 11 + -29 = -18 9y = -18 Divide each side by '9'. y = -2 Simplifying y = -2
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