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Simplifying 13 + -1[2 + 9y + -4(y + 4)] = -4(3y + -3) + -1[6(y + -1) + -5y + 7] Reorder the terms: 13 + -1[2 + 9y + -4(4 + y)] = -4(3y + -3) + -1[6(y + -1) + -5y + 7] 13 + -1[2 + 9y + (4 * -4 + y * -4)] = -4(3y + -3) + -1[6(y + -1) + -5y + 7] 13 + -1[2 + 9y + (-16 + -4y)] = -4(3y + -3) + -1[6(y + -1) + -5y + 7] Reorder the terms: 13 + -1[2 + -16 + 9y + -4y] = -4(3y + -3) + -1[6(y + -1) + -5y + 7] Combine like terms: 2 + -16 = -14 13 + -1[-14 + 9y + -4y] = -4(3y + -3) + -1[6(y + -1) + -5y + 7] Combine like terms: 9y + -4y = 5y 13 + -1[-14 + 5y] = -4(3y + -3) + -1[6(y + -1) + -5y + 7] 13 + [-14 * -1 + 5y * -1] = -4(3y + -3) + -1[6(y + -1) + -5y + 7] 13 + [14 + -5y] = -4(3y + -3) + -1[6(y + -1) + -5y + 7] Combine like terms: 13 + 14 = 27 27 + -5y = -4(3y + -3) + -1[6(y + -1) + -5y + 7] Reorder the terms: 27 + -5y = -4(-3 + 3y) + -1[6(y + -1) + -5y + 7] 27 + -5y = (-3 * -4 + 3y * -4) + -1[6(y + -1) + -5y + 7] 27 + -5y = (12 + -12y) + -1[6(y + -1) + -5y + 7] Reorder the terms: 27 + -5y = 12 + -12y + -1[6(-1 + y) + -5y + 7] 27 + -5y = 12 + -12y + -1[(-1 * 6 + y * 6) + -5y + 7] 27 + -5y = 12 + -12y + -1[(-6 + 6y) + -5y + 7] Reorder the terms: 27 + -5y = 12 + -12y + -1[-6 + 7 + 6y + -5y] Combine like terms: -6 + 7 = 1 27 + -5y = 12 + -12y + -1[1 + 6y + -5y] Combine like terms: 6y + -5y = 1y 27 + -5y = 12 + -12y + -1[1 + 1y] 27 + -5y = 12 + -12y + [1 * -1 + 1y * -1] 27 + -5y = 12 + -12y + [-1 + -1y] Reorder the terms: 27 + -5y = 12 + -1 + -12y + -1y Combine like terms: 12 + -1 = 11 27 + -5y = 11 + -12y + -1y Combine like terms: -12y + -1y = -13y 27 + -5y = 11 + -13y Solving 27 + -5y = 11 + -13y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '13y' to each side of the equation. 27 + -5y + 13y = 11 + -13y + 13y Combine like terms: -5y + 13y = 8y 27 + 8y = 11 + -13y + 13y Combine like terms: -13y + 13y = 0 27 + 8y = 11 + 0 27 + 8y = 11 Add '-27' to each side of the equation. 27 + -27 + 8y = 11 + -27 Combine like terms: 27 + -27 = 0 0 + 8y = 11 + -27 8y = 11 + -27 Combine like terms: 11 + -27 = -16 8y = -16 Divide each side by '8'. y = -2 Simplifying y = -2
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