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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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