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Simplifying 34 + -1[3 + 4y + -2(y + 4)] = -5(4y + -7) + -1[7(y + -1) + -22y + 27] Reorder the terms: 34 + -1[3 + 4y + -2(4 + y)] = -5(4y + -7) + -1[7(y + -1) + -22y + 27] 34 + -1[3 + 4y + (4 * -2 + y * -2)] = -5(4y + -7) + -1[7(y + -1) + -22y + 27] 34 + -1[3 + 4y + (-8 + -2y)] = -5(4y + -7) + -1[7(y + -1) + -22y + 27] Reorder the terms: 34 + -1[3 + -8 + 4y + -2y] = -5(4y + -7) + -1[7(y + -1) + -22y + 27] Combine like terms: 3 + -8 = -5 34 + -1[-5 + 4y + -2y] = -5(4y + -7) + -1[7(y + -1) + -22y + 27] Combine like terms: 4y + -2y = 2y 34 + -1[-5 + 2y] = -5(4y + -7) + -1[7(y + -1) + -22y + 27] 34 + [-5 * -1 + 2y * -1] = -5(4y + -7) + -1[7(y + -1) + -22y + 27] 34 + [5 + -2y] = -5(4y + -7) + -1[7(y + -1) + -22y + 27] Combine like terms: 34 + 5 = 39 39 + -2y = -5(4y + -7) + -1[7(y + -1) + -22y + 27] Reorder the terms: 39 + -2y = -5(-7 + 4y) + -1[7(y + -1) + -22y + 27] 39 + -2y = (-7 * -5 + 4y * -5) + -1[7(y + -1) + -22y + 27] 39 + -2y = (35 + -20y) + -1[7(y + -1) + -22y + 27] Reorder the terms: 39 + -2y = 35 + -20y + -1[7(-1 + y) + -22y + 27] 39 + -2y = 35 + -20y + -1[(-1 * 7 + y * 7) + -22y + 27] 39 + -2y = 35 + -20y + -1[(-7 + 7y) + -22y + 27] Reorder the terms: 39 + -2y = 35 + -20y + -1[-7 + 27 + 7y + -22y] Combine like terms: -7 + 27 = 20 39 + -2y = 35 + -20y + -1[20 + 7y + -22y] Combine like terms: 7y + -22y = -15y 39 + -2y = 35 + -20y + -1[20 + -15y] 39 + -2y = 35 + -20y + [20 * -1 + -15y * -1] 39 + -2y = 35 + -20y + [-20 + 15y] Reorder the terms: 39 + -2y = 35 + -20 + -20y + 15y Combine like terms: 35 + -20 = 15 39 + -2y = 15 + -20y + 15y Combine like terms: -20y + 15y = -5y 39 + -2y = 15 + -5y Solving 39 + -2y = 15 + -5y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5y' to each side of the equation. 39 + -2y + 5y = 15 + -5y + 5y Combine like terms: -2y + 5y = 3y 39 + 3y = 15 + -5y + 5y Combine like terms: -5y + 5y = 0 39 + 3y = 15 + 0 39 + 3y = 15 Add '-39' to each side of the equation. 39 + -39 + 3y = 15 + -39 Combine like terms: 39 + -39 = 0 0 + 3y = 15 + -39 3y = 15 + -39 Combine like terms: 15 + -39 = -24 3y = -24 Divide each side by '3'. y = -8 Simplifying y = -8
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