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Simplifying 22 + -1[1 + 8y + -4(y + 5)] = -5(2y + -7) + -1[8(y + -1) + -9y + 27] Reorder the terms: 22 + -1[1 + 8y + -4(5 + y)] = -5(2y + -7) + -1[8(y + -1) + -9y + 27] 22 + -1[1 + 8y + (5 * -4 + y * -4)] = -5(2y + -7) + -1[8(y + -1) + -9y + 27] 22 + -1[1 + 8y + (-20 + -4y)] = -5(2y + -7) + -1[8(y + -1) + -9y + 27] Reorder the terms: 22 + -1[1 + -20 + 8y + -4y] = -5(2y + -7) + -1[8(y + -1) + -9y + 27] Combine like terms: 1 + -20 = -19 22 + -1[-19 + 8y + -4y] = -5(2y + -7) + -1[8(y + -1) + -9y + 27] Combine like terms: 8y + -4y = 4y 22 + -1[-19 + 4y] = -5(2y + -7) + -1[8(y + -1) + -9y + 27] 22 + [-19 * -1 + 4y * -1] = -5(2y + -7) + -1[8(y + -1) + -9y + 27] 22 + [19 + -4y] = -5(2y + -7) + -1[8(y + -1) + -9y + 27] Combine like terms: 22 + 19 = 41 41 + -4y = -5(2y + -7) + -1[8(y + -1) + -9y + 27] Reorder the terms: 41 + -4y = -5(-7 + 2y) + -1[8(y + -1) + -9y + 27] 41 + -4y = (-7 * -5 + 2y * -5) + -1[8(y + -1) + -9y + 27] 41 + -4y = (35 + -10y) + -1[8(y + -1) + -9y + 27] Reorder the terms: 41 + -4y = 35 + -10y + -1[8(-1 + y) + -9y + 27] 41 + -4y = 35 + -10y + -1[(-1 * 8 + y * 8) + -9y + 27] 41 + -4y = 35 + -10y + -1[(-8 + 8y) + -9y + 27] Reorder the terms: 41 + -4y = 35 + -10y + -1[-8 + 27 + 8y + -9y] Combine like terms: -8 + 27 = 19 41 + -4y = 35 + -10y + -1[19 + 8y + -9y] Combine like terms: 8y + -9y = -1y 41 + -4y = 35 + -10y + -1[19 + -1y] 41 + -4y = 35 + -10y + [19 * -1 + -1y * -1] 41 + -4y = 35 + -10y + [-19 + 1y] Reorder the terms: 41 + -4y = 35 + -19 + -10y + 1y Combine like terms: 35 + -19 = 16 41 + -4y = 16 + -10y + 1y Combine like terms: -10y + 1y = -9y 41 + -4y = 16 + -9y Solving 41 + -4y = 16 + -9y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9y' to each side of the equation. 41 + -4y + 9y = 16 + -9y + 9y Combine like terms: -4y + 9y = 5y 41 + 5y = 16 + -9y + 9y Combine like terms: -9y + 9y = 0 41 + 5y = 16 + 0 41 + 5y = 16 Add '-41' to each side of the equation. 41 + -41 + 5y = 16 + -41 Combine like terms: 41 + -41 = 0 0 + 5y = 16 + -41 5y = 16 + -41 Combine like terms: 16 + -41 = -25 5y = -25 Divide each side by '5'. y = -5 Simplifying y = -5
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