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Simplifying 41 + -1[4 + 8y + -3(y + 2)] = -4(4y + -5) + -1[7(y + -1) + -14y + 12] Reorder the terms: 41 + -1[4 + 8y + -3(2 + y)] = -4(4y + -5) + -1[7(y + -1) + -14y + 12] 41 + -1[4 + 8y + (2 * -3 + y * -3)] = -4(4y + -5) + -1[7(y + -1) + -14y + 12] 41 + -1[4 + 8y + (-6 + -3y)] = -4(4y + -5) + -1[7(y + -1) + -14y + 12] Reorder the terms: 41 + -1[4 + -6 + 8y + -3y] = -4(4y + -5) + -1[7(y + -1) + -14y + 12] Combine like terms: 4 + -6 = -2 41 + -1[-2 + 8y + -3y] = -4(4y + -5) + -1[7(y + -1) + -14y + 12] Combine like terms: 8y + -3y = 5y 41 + -1[-2 + 5y] = -4(4y + -5) + -1[7(y + -1) + -14y + 12] 41 + [-2 * -1 + 5y * -1] = -4(4y + -5) + -1[7(y + -1) + -14y + 12] 41 + [2 + -5y] = -4(4y + -5) + -1[7(y + -1) + -14y + 12] Combine like terms: 41 + 2 = 43 43 + -5y = -4(4y + -5) + -1[7(y + -1) + -14y + 12] Reorder the terms: 43 + -5y = -4(-5 + 4y) + -1[7(y + -1) + -14y + 12] 43 + -5y = (-5 * -4 + 4y * -4) + -1[7(y + -1) + -14y + 12] 43 + -5y = (20 + -16y) + -1[7(y + -1) + -14y + 12] Reorder the terms: 43 + -5y = 20 + -16y + -1[7(-1 + y) + -14y + 12] 43 + -5y = 20 + -16y + -1[(-1 * 7 + y * 7) + -14y + 12] 43 + -5y = 20 + -16y + -1[(-7 + 7y) + -14y + 12] Reorder the terms: 43 + -5y = 20 + -16y + -1[-7 + 12 + 7y + -14y] Combine like terms: -7 + 12 = 5 43 + -5y = 20 + -16y + -1[5 + 7y + -14y] Combine like terms: 7y + -14y = -7y 43 + -5y = 20 + -16y + -1[5 + -7y] 43 + -5y = 20 + -16y + [5 * -1 + -7y * -1] 43 + -5y = 20 + -16y + [-5 + 7y] Reorder the terms: 43 + -5y = 20 + -5 + -16y + 7y Combine like terms: 20 + -5 = 15 43 + -5y = 15 + -16y + 7y Combine like terms: -16y + 7y = -9y 43 + -5y = 15 + -9y Solving 43 + -5y = 15 + -9y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9y' to each side of the equation. 43 + -5y + 9y = 15 + -9y + 9y Combine like terms: -5y + 9y = 4y 43 + 4y = 15 + -9y + 9y Combine like terms: -9y + 9y = 0 43 + 4y = 15 + 0 43 + 4y = 15 Add '-43' to each side of the equation. 43 + -43 + 4y = 15 + -43 Combine like terms: 43 + -43 = 0 0 + 4y = 15 + -43 4y = 15 + -43 Combine like terms: 15 + -43 = -28 4y = -28 Divide each side by '4'. y = -7 Simplifying y = -7
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