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Simplifying 31 + -1[4 + 6y + -2(y + 4)] = 5(5y + -7) + -1[9(y + -1) + -24y + 33] Reorder the terms: 31 + -1[4 + 6y + -2(4 + y)] = 5(5y + -7) + -1[9(y + -1) + -24y + 33] 31 + -1[4 + 6y + (4 * -2 + y * -2)] = 5(5y + -7) + -1[9(y + -1) + -24y + 33] 31 + -1[4 + 6y + (-8 + -2y)] = 5(5y + -7) + -1[9(y + -1) + -24y + 33] Reorder the terms: 31 + -1[4 + -8 + 6y + -2y] = 5(5y + -7) + -1[9(y + -1) + -24y + 33] Combine like terms: 4 + -8 = -4 31 + -1[-4 + 6y + -2y] = 5(5y + -7) + -1[9(y + -1) + -24y + 33] Combine like terms: 6y + -2y = 4y 31 + -1[-4 + 4y] = 5(5y + -7) + -1[9(y + -1) + -24y + 33] 31 + [-4 * -1 + 4y * -1] = 5(5y + -7) + -1[9(y + -1) + -24y + 33] 31 + [4 + -4y] = 5(5y + -7) + -1[9(y + -1) + -24y + 33] Combine like terms: 31 + 4 = 35 35 + -4y = 5(5y + -7) + -1[9(y + -1) + -24y + 33] Reorder the terms: 35 + -4y = 5(-7 + 5y) + -1[9(y + -1) + -24y + 33] 35 + -4y = (-7 * 5 + 5y * 5) + -1[9(y + -1) + -24y + 33] 35 + -4y = (-35 + 25y) + -1[9(y + -1) + -24y + 33] Reorder the terms: 35 + -4y = -35 + 25y + -1[9(-1 + y) + -24y + 33] 35 + -4y = -35 + 25y + -1[(-1 * 9 + y * 9) + -24y + 33] 35 + -4y = -35 + 25y + -1[(-9 + 9y) + -24y + 33] Reorder the terms: 35 + -4y = -35 + 25y + -1[-9 + 33 + 9y + -24y] Combine like terms: -9 + 33 = 24 35 + -4y = -35 + 25y + -1[24 + 9y + -24y] Combine like terms: 9y + -24y = -15y 35 + -4y = -35 + 25y + -1[24 + -15y] 35 + -4y = -35 + 25y + [24 * -1 + -15y * -1] 35 + -4y = -35 + 25y + [-24 + 15y] Reorder the terms: 35 + -4y = -35 + -24 + 25y + 15y Combine like terms: -35 + -24 = -59 35 + -4y = -59 + 25y + 15y Combine like terms: 25y + 15y = 40y 35 + -4y = -59 + 40y Solving 35 + -4y = -59 + 40y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-40y' to each side of the equation. 35 + -4y + -40y = -59 + 40y + -40y Combine like terms: -4y + -40y = -44y 35 + -44y = -59 + 40y + -40y Combine like terms: 40y + -40y = 0 35 + -44y = -59 + 0 35 + -44y = -59 Add '-35' to each side of the equation. 35 + -35 + -44y = -59 + -35 Combine like terms: 35 + -35 = 0 0 + -44y = -59 + -35 -44y = -59 + -35 Combine like terms: -59 + -35 = -94 -44y = -94 Divide each side by '-44'. y = 2.136363636 Simplifying y = 2.136363636
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