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Simplifying 34 + -1[5 + 5y + -3(y + 2)] = -5(2y + -7) + -1[7(y + -1) + -9y + 25] Reorder the terms: 34 + -1[5 + 5y + -3(2 + y)] = -5(2y + -7) + -1[7(y + -1) + -9y + 25] 34 + -1[5 + 5y + (2 * -3 + y * -3)] = -5(2y + -7) + -1[7(y + -1) + -9y + 25] 34 + -1[5 + 5y + (-6 + -3y)] = -5(2y + -7) + -1[7(y + -1) + -9y + 25] Reorder the terms: 34 + -1[5 + -6 + 5y + -3y] = -5(2y + -7) + -1[7(y + -1) + -9y + 25] Combine like terms: 5 + -6 = -1 34 + -1[-1 + 5y + -3y] = -5(2y + -7) + -1[7(y + -1) + -9y + 25] Combine like terms: 5y + -3y = 2y 34 + -1[-1 + 2y] = -5(2y + -7) + -1[7(y + -1) + -9y + 25] 34 + [-1 * -1 + 2y * -1] = -5(2y + -7) + -1[7(y + -1) + -9y + 25] 34 + [1 + -2y] = -5(2y + -7) + -1[7(y + -1) + -9y + 25] Combine like terms: 34 + 1 = 35 35 + -2y = -5(2y + -7) + -1[7(y + -1) + -9y + 25] Reorder the terms: 35 + -2y = -5(-7 + 2y) + -1[7(y + -1) + -9y + 25] 35 + -2y = (-7 * -5 + 2y * -5) + -1[7(y + -1) + -9y + 25] 35 + -2y = (35 + -10y) + -1[7(y + -1) + -9y + 25] Reorder the terms: 35 + -2y = 35 + -10y + -1[7(-1 + y) + -9y + 25] 35 + -2y = 35 + -10y + -1[(-1 * 7 + y * 7) + -9y + 25] 35 + -2y = 35 + -10y + -1[(-7 + 7y) + -9y + 25] Reorder the terms: 35 + -2y = 35 + -10y + -1[-7 + 25 + 7y + -9y] Combine like terms: -7 + 25 = 18 35 + -2y = 35 + -10y + -1[18 + 7y + -9y] Combine like terms: 7y + -9y = -2y 35 + -2y = 35 + -10y + -1[18 + -2y] 35 + -2y = 35 + -10y + [18 * -1 + -2y * -1] 35 + -2y = 35 + -10y + [-18 + 2y] Reorder the terms: 35 + -2y = 35 + -18 + -10y + 2y Combine like terms: 35 + -18 = 17 35 + -2y = 17 + -10y + 2y Combine like terms: -10y + 2y = -8y 35 + -2y = 17 + -8y Solving 35 + -2y = 17 + -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. 35 + -2y + 8y = 17 + -8y + 8y Combine like terms: -2y + 8y = 6y 35 + 6y = 17 + -8y + 8y Combine like terms: -8y + 8y = 0 35 + 6y = 17 + 0 35 + 6y = 17 Add '-35' to each side of the equation. 35 + -35 + 6y = 17 + -35 Combine like terms: 35 + -35 = 0 0 + 6y = 17 + -35 6y = 17 + -35 Combine like terms: 17 + -35 = -18 6y = -18 Divide each side by '6'. y = -3 Simplifying y = -3
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