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Simplifying -47 + -1[2 + 5y + -9(y + 2)] = -11(2y + -5) + -1[7(y + -1) + -3y + 3] Reorder the terms: -47 + -1[2 + 5y + -9(2 + y)] = -11(2y + -5) + -1[7(y + -1) + -3y + 3] -47 + -1[2 + 5y + (2 * -9 + y * -9)] = -11(2y + -5) + -1[7(y + -1) + -3y + 3] -47 + -1[2 + 5y + (-18 + -9y)] = -11(2y + -5) + -1[7(y + -1) + -3y + 3] Reorder the terms: -47 + -1[2 + -18 + 5y + -9y] = -11(2y + -5) + -1[7(y + -1) + -3y + 3] Combine like terms: 2 + -18 = -16 -47 + -1[-16 + 5y + -9y] = -11(2y + -5) + -1[7(y + -1) + -3y + 3] Combine like terms: 5y + -9y = -4y -47 + -1[-16 + -4y] = -11(2y + -5) + -1[7(y + -1) + -3y + 3] -47 + [-16 * -1 + -4y * -1] = -11(2y + -5) + -1[7(y + -1) + -3y + 3] -47 + [16 + 4y] = -11(2y + -5) + -1[7(y + -1) + -3y + 3] Combine like terms: -47 + 16 = -31 -31 + 4y = -11(2y + -5) + -1[7(y + -1) + -3y + 3] Reorder the terms: -31 + 4y = -11(-5 + 2y) + -1[7(y + -1) + -3y + 3] -31 + 4y = (-5 * -11 + 2y * -11) + -1[7(y + -1) + -3y + 3] -31 + 4y = (55 + -22y) + -1[7(y + -1) + -3y + 3] Reorder the terms: -31 + 4y = 55 + -22y + -1[7(-1 + y) + -3y + 3] -31 + 4y = 55 + -22y + -1[(-1 * 7 + y * 7) + -3y + 3] -31 + 4y = 55 + -22y + -1[(-7 + 7y) + -3y + 3] Reorder the terms: -31 + 4y = 55 + -22y + -1[-7 + 3 + 7y + -3y] Combine like terms: -7 + 3 = -4 -31 + 4y = 55 + -22y + -1[-4 + 7y + -3y] Combine like terms: 7y + -3y = 4y -31 + 4y = 55 + -22y + -1[-4 + 4y] -31 + 4y = 55 + -22y + [-4 * -1 + 4y * -1] -31 + 4y = 55 + -22y + [4 + -4y] Reorder the terms: -31 + 4y = 55 + 4 + -22y + -4y Combine like terms: 55 + 4 = 59 -31 + 4y = 59 + -22y + -4y Combine like terms: -22y + -4y = -26y -31 + 4y = 59 + -26y Solving -31 + 4y = 59 + -26y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '26y' to each side of the equation. -31 + 4y + 26y = 59 + -26y + 26y Combine like terms: 4y + 26y = 30y -31 + 30y = 59 + -26y + 26y Combine like terms: -26y + 26y = 0 -31 + 30y = 59 + 0 -31 + 30y = 59 Add '31' to each side of the equation. -31 + 31 + 30y = 59 + 31 Combine like terms: -31 + 31 = 0 0 + 30y = 59 + 31 30y = 59 + 31 Combine like terms: 59 + 31 = 90 30y = 90 Divide each side by '30'. y = 3 Simplifying y = 3
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