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Simplifying 50 + -1[1 + 8y + -2(y + 5)] = -3(5y + -7) + -1[6(y + -1) + -9y + 10] Reorder the terms: 50 + -1[1 + 8y + -2(5 + y)] = -3(5y + -7) + -1[6(y + -1) + -9y + 10] 50 + -1[1 + 8y + (5 * -2 + y * -2)] = -3(5y + -7) + -1[6(y + -1) + -9y + 10] 50 + -1[1 + 8y + (-10 + -2y)] = -3(5y + -7) + -1[6(y + -1) + -9y + 10] Reorder the terms: 50 + -1[1 + -10 + 8y + -2y] = -3(5y + -7) + -1[6(y + -1) + -9y + 10] Combine like terms: 1 + -10 = -9 50 + -1[-9 + 8y + -2y] = -3(5y + -7) + -1[6(y + -1) + -9y + 10] Combine like terms: 8y + -2y = 6y 50 + -1[-9 + 6y] = -3(5y + -7) + -1[6(y + -1) + -9y + 10] 50 + [-9 * -1 + 6y * -1] = -3(5y + -7) + -1[6(y + -1) + -9y + 10] 50 + [9 + -6y] = -3(5y + -7) + -1[6(y + -1) + -9y + 10] Combine like terms: 50 + 9 = 59 59 + -6y = -3(5y + -7) + -1[6(y + -1) + -9y + 10] Reorder the terms: 59 + -6y = -3(-7 + 5y) + -1[6(y + -1) + -9y + 10] 59 + -6y = (-7 * -3 + 5y * -3) + -1[6(y + -1) + -9y + 10] 59 + -6y = (21 + -15y) + -1[6(y + -1) + -9y + 10] Reorder the terms: 59 + -6y = 21 + -15y + -1[6(-1 + y) + -9y + 10] 59 + -6y = 21 + -15y + -1[(-1 * 6 + y * 6) + -9y + 10] 59 + -6y = 21 + -15y + -1[(-6 + 6y) + -9y + 10] Reorder the terms: 59 + -6y = 21 + -15y + -1[-6 + 10 + 6y + -9y] Combine like terms: -6 + 10 = 4 59 + -6y = 21 + -15y + -1[4 + 6y + -9y] Combine like terms: 6y + -9y = -3y 59 + -6y = 21 + -15y + -1[4 + -3y] 59 + -6y = 21 + -15y + [4 * -1 + -3y * -1] 59 + -6y = 21 + -15y + [-4 + 3y] Reorder the terms: 59 + -6y = 21 + -4 + -15y + 3y Combine like terms: 21 + -4 = 17 59 + -6y = 17 + -15y + 3y Combine like terms: -15y + 3y = -12y 59 + -6y = 17 + -12y Solving 59 + -6y = 17 + -12y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12y' to each side of the equation. 59 + -6y + 12y = 17 + -12y + 12y Combine like terms: -6y + 12y = 6y 59 + 6y = 17 + -12y + 12y Combine like terms: -12y + 12y = 0 59 + 6y = 17 + 0 59 + 6y = 17 Add '-59' to each side of the equation. 59 + -59 + 6y = 17 + -59 Combine like terms: 59 + -59 = 0 0 + 6y = 17 + -59 6y = 17 + -59 Combine like terms: 17 + -59 = -42 6y = -42 Divide each side by '6'. y = -7 Simplifying y = -7
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