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Simplifying 32 + -1[2 + 9y + -3(y + 5)] = -5(5y + -3) + -1[(y + -1) + -18 + 4] Reorder the terms: 32 + -1[2 + 9y + -3(5 + y)] = -5(5y + -3) + -1[(y + -1) + -18 + 4] 32 + -1[2 + 9y + (5 * -3 + y * -3)] = -5(5y + -3) + -1[(y + -1) + -18 + 4] 32 + -1[2 + 9y + (-15 + -3y)] = -5(5y + -3) + -1[(y + -1) + -18 + 4] Reorder the terms: 32 + -1[2 + -15 + 9y + -3y] = -5(5y + -3) + -1[(y + -1) + -18 + 4] Combine like terms: 2 + -15 = -13 32 + -1[-13 + 9y + -3y] = -5(5y + -3) + -1[(y + -1) + -18 + 4] Combine like terms: 9y + -3y = 6y 32 + -1[-13 + 6y] = -5(5y + -3) + -1[(y + -1) + -18 + 4] 32 + [-13 * -1 + 6y * -1] = -5(5y + -3) + -1[(y + -1) + -18 + 4] 32 + [13 + -6y] = -5(5y + -3) + -1[(y + -1) + -18 + 4] Combine like terms: 32 + 13 = 45 45 + -6y = -5(5y + -3) + -1[(y + -1) + -18 + 4] Reorder the terms: 45 + -6y = -5(-3 + 5y) + -1[(y + -1) + -18 + 4] 45 + -6y = (-3 * -5 + 5y * -5) + -1[(y + -1) + -18 + 4] 45 + -6y = (15 + -25y) + -1[(y + -1) + -18 + 4] Reorder the terms: 45 + -6y = 15 + -25y + -1[(-1 + y) + -18 + 4] Remove parenthesis around (-1 + y) 45 + -6y = 15 + -25y + -1[-1 + y + -18 + 4] Reorder the terms: 45 + -6y = 15 + -25y + -1[-1 + -18 + 4 + y] Combine like terms: -1 + -18 = -19 45 + -6y = 15 + -25y + -1[-19 + 4 + y] Combine like terms: -19 + 4 = -15 45 + -6y = 15 + -25y + -1[-15 + y] 45 + -6y = 15 + -25y + [-15 * -1 + y * -1] 45 + -6y = 15 + -25y + [15 + -1y] Reorder the terms: 45 + -6y = 15 + 15 + -25y + -1y Combine like terms: 15 + 15 = 30 45 + -6y = 30 + -25y + -1y Combine like terms: -25y + -1y = -26y 45 + -6y = 30 + -26y Solving 45 + -6y = 30 + -26y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '26y' to each side of the equation. 45 + -6y + 26y = 30 + -26y + 26y Combine like terms: -6y + 26y = 20y 45 + 20y = 30 + -26y + 26y Combine like terms: -26y + 26y = 0 45 + 20y = 30 + 0 45 + 20y = 30 Add '-45' to each side of the equation. 45 + -45 + 20y = 30 + -45 Combine like terms: 45 + -45 = 0 0 + 20y = 30 + -45 20y = 30 + -45 Combine like terms: 30 + -45 = -15 20y = -15 Divide each side by '20'. y = -0.75 Simplifying y = -0.75
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