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Simplifying -2(y + -1) + (-4(y + -1) + -5[y + -2(4 + -1y) + 3y] + -1(y + 1)) = 2y + -1(-5 + -1y) Reorder the terms: -2(-1 + y) + (-4(y + -1) + -5[y + -2(4 + -1y) + 3y] + -1(y + 1)) = 2y + -1(-5 + -1y) (-1 * -2 + y * -2) + (-4(y + -1) + -5[y + -2(4 + -1y) + 3y] + -1(y + 1)) = 2y + -1(-5 + -1y) (2 + -2y) + (-4(y + -1) + -5[y + -2(4 + -1y) + 3y] + -1(y + 1)) = 2y + -1(-5 + -1y) Reorder the terms: 2 + -2y + (-4(-1 + y) + -5[y + -2(4 + -1y) + 3y] + -1(y + 1)) = 2y + -1(-5 + -1y) 2 + -2y + ((-1 * -4 + y * -4) + -5[y + -2(4 + -1y) + 3y] + -1(y + 1)) = 2y + -1(-5 + -1y) 2 + -2y + ((4 + -4y) + -5[y + -2(4 + -1y) + 3y] + -1(y + 1)) = 2y + -1(-5 + -1y) 2 + -2y + (4 + -4y + -5[y + (4 * -2 + -1y * -2) + 3y] + -1(y + 1)) = 2y + -1(-5 + -1y) 2 + -2y + (4 + -4y + -5[y + (-8 + 2y) + 3y] + -1(y + 1)) = 2y + -1(-5 + -1y) Reorder the terms: 2 + -2y + (4 + -4y + -5[-8 + y + 2y + 3y] + -1(y + 1)) = 2y + -1(-5 + -1y) Combine like terms: y + 2y = 3y 2 + -2y + (4 + -4y + -5[-8 + 3y + 3y] + -1(y + 1)) = 2y + -1(-5 + -1y) Combine like terms: 3y + 3y = 6y 2 + -2y + (4 + -4y + -5[-8 + 6y] + -1(y + 1)) = 2y + -1(-5 + -1y) 2 + -2y + (4 + -4y + [-8 * -5 + 6y * -5] + -1(y + 1)) = 2y + -1(-5 + -1y) 2 + -2y + (4 + -4y + [40 + -30y] + -1(y + 1)) = 2y + -1(-5 + -1y) Reorder the terms: 2 + -2y + (4 + -4y + 40 + -30y + -1(1 + y)) = 2y + -1(-5 + -1y) 2 + -2y + (4 + -4y + 40 + -30y + (1 * -1 + y * -1)) = 2y + -1(-5 + -1y) 2 + -2y + (4 + -4y + 40 + -30y + (-1 + -1y)) = 2y + -1(-5 + -1y) Reorder the terms: 2 + -2y + (4 + 40 + -1 + -4y + -30y + -1y) = 2y + -1(-5 + -1y) Combine like terms: 4 + 40 = 44 2 + -2y + (44 + -1 + -4y + -30y + -1y) = 2y + -1(-5 + -1y) Combine like terms: 44 + -1 = 43 2 + -2y + (43 + -4y + -30y + -1y) = 2y + -1(-5 + -1y) Combine like terms: -4y + -30y = -34y 2 + -2y + (43 + -34y + -1y) = 2y + -1(-5 + -1y) Combine like terms: -34y + -1y = -35y 2 + -2y + (43 + -35y) = 2y + -1(-5 + -1y) Remove parenthesis around (43 + -35y) 2 + -2y + 43 + -35y = 2y + -1(-5 + -1y) Reorder the terms: 2 + 43 + -2y + -35y = 2y + -1(-5 + -1y) Combine like terms: 2 + 43 = 45 45 + -2y + -35y = 2y + -1(-5 + -1y) Combine like terms: -2y + -35y = -37y 45 + -37y = 2y + -1(-5 + -1y) 45 + -37y = 2y + (-5 * -1 + -1y * -1) 45 + -37y = 2y + (5 + 1y) Reorder the terms: 45 + -37y = 5 + 2y + 1y Combine like terms: 2y + 1y = 3y 45 + -37y = 5 + 3y Solving 45 + -37y = 5 + 3y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3y' to each side of the equation. 45 + -37y + -3y = 5 + 3y + -3y Combine like terms: -37y + -3y = -40y 45 + -40y = 5 + 3y + -3y Combine like terms: 3y + -3y = 0 45 + -40y = 5 + 0 45 + -40y = 5 Add '-45' to each side of the equation. 45 + -45 + -40y = 5 + -45 Combine like terms: 45 + -45 = 0 0 + -40y = 5 + -45 -40y = 5 + -45 Combine like terms: 5 + -45 = -40 -40y = -40 Divide each side by '-40'. y = 1 Simplifying y = 1
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