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Simplifying 35 + -1(1 + 9y + -4(y + 2)) = -4(4y + -4) + -1(5(y + -1) + -9y + 7) Reorder the terms: 35 + -1(1 + 9y + -4(2 + y)) = -4(4y + -4) + -1(5(y + -1) + -9y + 7) 35 + -1(1 + 9y + (2 * -4 + y * -4)) = -4(4y + -4) + -1(5(y + -1) + -9y + 7) 35 + -1(1 + 9y + (-8 + -4y)) = -4(4y + -4) + -1(5(y + -1) + -9y + 7) Reorder the terms: 35 + -1(1 + -8 + 9y + -4y) = -4(4y + -4) + -1(5(y + -1) + -9y + 7) Combine like terms: 1 + -8 = -7 35 + -1(-7 + 9y + -4y) = -4(4y + -4) + -1(5(y + -1) + -9y + 7) Combine like terms: 9y + -4y = 5y 35 + -1(-7 + 5y) = -4(4y + -4) + -1(5(y + -1) + -9y + 7) 35 + (-7 * -1 + 5y * -1) = -4(4y + -4) + -1(5(y + -1) + -9y + 7) 35 + (7 + -5y) = -4(4y + -4) + -1(5(y + -1) + -9y + 7) Combine like terms: 35 + 7 = 42 42 + -5y = -4(4y + -4) + -1(5(y + -1) + -9y + 7) Reorder the terms: 42 + -5y = -4(-4 + 4y) + -1(5(y + -1) + -9y + 7) 42 + -5y = (-4 * -4 + 4y * -4) + -1(5(y + -1) + -9y + 7) 42 + -5y = (16 + -16y) + -1(5(y + -1) + -9y + 7) Reorder the terms: 42 + -5y = 16 + -16y + -1(5(-1 + y) + -9y + 7) 42 + -5y = 16 + -16y + -1((-1 * 5 + y * 5) + -9y + 7) 42 + -5y = 16 + -16y + -1((-5 + 5y) + -9y + 7) Reorder the terms: 42 + -5y = 16 + -16y + -1(-5 + 7 + 5y + -9y) Combine like terms: -5 + 7 = 2 42 + -5y = 16 + -16y + -1(2 + 5y + -9y) Combine like terms: 5y + -9y = -4y 42 + -5y = 16 + -16y + -1(2 + -4y) 42 + -5y = 16 + -16y + (2 * -1 + -4y * -1) 42 + -5y = 16 + -16y + (-2 + 4y) Reorder the terms: 42 + -5y = 16 + -2 + -16y + 4y Combine like terms: 16 + -2 = 14 42 + -5y = 14 + -16y + 4y Combine like terms: -16y + 4y = -12y 42 + -5y = 14 + -12y Solving 42 + -5y = 14 + -12y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12y' to each side of the equation. 42 + -5y + 12y = 14 + -12y + 12y Combine like terms: -5y + 12y = 7y 42 + 7y = 14 + -12y + 12y Combine like terms: -12y + 12y = 0 42 + 7y = 14 + 0 42 + 7y = 14 Add '-42' to each side of the equation. 42 + -42 + 7y = 14 + -42 Combine like terms: 42 + -42 = 0 0 + 7y = 14 + -42 7y = 14 + -42 Combine like terms: 14 + -42 = -28 7y = -28 Divide each side by '7'. y = -4 Simplifying y = -4
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