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Simplifying 21 + -1[1 + 5y + -2(y + 2)] = -5(2y + -3) + -1[8(y + -1) + -10y + 9] Reorder the terms: 21 + -1[1 + 5y + -2(2 + y)] = -5(2y + -3) + -1[8(y + -1) + -10y + 9] 21 + -1[1 + 5y + (2 * -2 + y * -2)] = -5(2y + -3) + -1[8(y + -1) + -10y + 9] 21 + -1[1 + 5y + (-4 + -2y)] = -5(2y + -3) + -1[8(y + -1) + -10y + 9] Reorder the terms: 21 + -1[1 + -4 + 5y + -2y] = -5(2y + -3) + -1[8(y + -1) + -10y + 9] Combine like terms: 1 + -4 = -3 21 + -1[-3 + 5y + -2y] = -5(2y + -3) + -1[8(y + -1) + -10y + 9] Combine like terms: 5y + -2y = 3y 21 + -1[-3 + 3y] = -5(2y + -3) + -1[8(y + -1) + -10y + 9] 21 + [-3 * -1 + 3y * -1] = -5(2y + -3) + -1[8(y + -1) + -10y + 9] 21 + [3 + -3y] = -5(2y + -3) + -1[8(y + -1) + -10y + 9] Combine like terms: 21 + 3 = 24 24 + -3y = -5(2y + -3) + -1[8(y + -1) + -10y + 9] Reorder the terms: 24 + -3y = -5(-3 + 2y) + -1[8(y + -1) + -10y + 9] 24 + -3y = (-3 * -5 + 2y * -5) + -1[8(y + -1) + -10y + 9] 24 + -3y = (15 + -10y) + -1[8(y + -1) + -10y + 9] Reorder the terms: 24 + -3y = 15 + -10y + -1[8(-1 + y) + -10y + 9] 24 + -3y = 15 + -10y + -1[(-1 * 8 + y * 8) + -10y + 9] 24 + -3y = 15 + -10y + -1[(-8 + 8y) + -10y + 9] Reorder the terms: 24 + -3y = 15 + -10y + -1[-8 + 9 + 8y + -10y] Combine like terms: -8 + 9 = 1 24 + -3y = 15 + -10y + -1[1 + 8y + -10y] Combine like terms: 8y + -10y = -2y 24 + -3y = 15 + -10y + -1[1 + -2y] 24 + -3y = 15 + -10y + [1 * -1 + -2y * -1] 24 + -3y = 15 + -10y + [-1 + 2y] Reorder the terms: 24 + -3y = 15 + -1 + -10y + 2y Combine like terms: 15 + -1 = 14 24 + -3y = 14 + -10y + 2y Combine like terms: -10y + 2y = -8y 24 + -3y = 14 + -8y Solving 24 + -3y = 14 + -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. 24 + -3y + 8y = 14 + -8y + 8y Combine like terms: -3y + 8y = 5y 24 + 5y = 14 + -8y + 8y Combine like terms: -8y + 8y = 0 24 + 5y = 14 + 0 24 + 5y = 14 Add '-24' to each side of the equation. 24 + -24 + 5y = 14 + -24 Combine like terms: 24 + -24 = 0 0 + 5y = 14 + -24 5y = 14 + -24 Combine like terms: 14 + -24 = -10 5y = -10 Divide each side by '5'. y = -2 Simplifying y = -2
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