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Simplifying 17 + -1[5 + 8y + -3(y + 2)] = -3(4y + -3) + -1[8(y + -1) + -13y + 3] Reorder the terms: 17 + -1[5 + 8y + -3(2 + y)] = -3(4y + -3) + -1[8(y + -1) + -13y + 3] 17 + -1[5 + 8y + (2 * -3 + y * -3)] = -3(4y + -3) + -1[8(y + -1) + -13y + 3] 17 + -1[5 + 8y + (-6 + -3y)] = -3(4y + -3) + -1[8(y + -1) + -13y + 3] Reorder the terms: 17 + -1[5 + -6 + 8y + -3y] = -3(4y + -3) + -1[8(y + -1) + -13y + 3] Combine like terms: 5 + -6 = -1 17 + -1[-1 + 8y + -3y] = -3(4y + -3) + -1[8(y + -1) + -13y + 3] Combine like terms: 8y + -3y = 5y 17 + -1[-1 + 5y] = -3(4y + -3) + -1[8(y + -1) + -13y + 3] 17 + [-1 * -1 + 5y * -1] = -3(4y + -3) + -1[8(y + -1) + -13y + 3] 17 + [1 + -5y] = -3(4y + -3) + -1[8(y + -1) + -13y + 3] Combine like terms: 17 + 1 = 18 18 + -5y = -3(4y + -3) + -1[8(y + -1) + -13y + 3] Reorder the terms: 18 + -5y = -3(-3 + 4y) + -1[8(y + -1) + -13y + 3] 18 + -5y = (-3 * -3 + 4y * -3) + -1[8(y + -1) + -13y + 3] 18 + -5y = (9 + -12y) + -1[8(y + -1) + -13y + 3] Reorder the terms: 18 + -5y = 9 + -12y + -1[8(-1 + y) + -13y + 3] 18 + -5y = 9 + -12y + -1[(-1 * 8 + y * 8) + -13y + 3] 18 + -5y = 9 + -12y + -1[(-8 + 8y) + -13y + 3] Reorder the terms: 18 + -5y = 9 + -12y + -1[-8 + 3 + 8y + -13y] Combine like terms: -8 + 3 = -5 18 + -5y = 9 + -12y + -1[-5 + 8y + -13y] Combine like terms: 8y + -13y = -5y 18 + -5y = 9 + -12y + -1[-5 + -5y] 18 + -5y = 9 + -12y + [-5 * -1 + -5y * -1] 18 + -5y = 9 + -12y + [5 + 5y] Reorder the terms: 18 + -5y = 9 + 5 + -12y + 5y Combine like terms: 9 + 5 = 14 18 + -5y = 14 + -12y + 5y Combine like terms: -12y + 5y = -7y 18 + -5y = 14 + -7y Solving 18 + -5y = 14 + -7y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7y' to each side of the equation. 18 + -5y + 7y = 14 + -7y + 7y Combine like terms: -5y + 7y = 2y 18 + 2y = 14 + -7y + 7y Combine like terms: -7y + 7y = 0 18 + 2y = 14 + 0 18 + 2y = 14 Add '-18' to each side of the equation. 18 + -18 + 2y = 14 + -18 Combine like terms: 18 + -18 = 0 0 + 2y = 14 + -18 2y = 14 + -18 Combine like terms: 14 + -18 = -4 2y = -4 Divide each side by '2'. y = -2 Simplifying y = -2
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