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Simplifying -41 + -1[2 + 5y + -9(y + 2)] = -5(2y + -5) + -1[7(y + -1) + -3y + 3] Reorder the terms: -41 + -1[2 + 5y + -9(2 + y)] = -5(2y + -5) + -1[7(y + -1) + -3y + 3] -41 + -1[2 + 5y + (2 * -9 + y * -9)] = -5(2y + -5) + -1[7(y + -1) + -3y + 3] -41 + -1[2 + 5y + (-18 + -9y)] = -5(2y + -5) + -1[7(y + -1) + -3y + 3] Reorder the terms: -41 + -1[2 + -18 + 5y + -9y] = -5(2y + -5) + -1[7(y + -1) + -3y + 3] Combine like terms: 2 + -18 = -16 -41 + -1[-16 + 5y + -9y] = -5(2y + -5) + -1[7(y + -1) + -3y + 3] Combine like terms: 5y + -9y = -4y -41 + -1[-16 + -4y] = -5(2y + -5) + -1[7(y + -1) + -3y + 3] -41 + [-16 * -1 + -4y * -1] = -5(2y + -5) + -1[7(y + -1) + -3y + 3] -41 + [16 + 4y] = -5(2y + -5) + -1[7(y + -1) + -3y + 3] Combine like terms: -41 + 16 = -25 -25 + 4y = -5(2y + -5) + -1[7(y + -1) + -3y + 3] Reorder the terms: -25 + 4y = -5(-5 + 2y) + -1[7(y + -1) + -3y + 3] -25 + 4y = (-5 * -5 + 2y * -5) + -1[7(y + -1) + -3y + 3] -25 + 4y = (25 + -10y) + -1[7(y + -1) + -3y + 3] Reorder the terms: -25 + 4y = 25 + -10y + -1[7(-1 + y) + -3y + 3] -25 + 4y = 25 + -10y + -1[(-1 * 7 + y * 7) + -3y + 3] -25 + 4y = 25 + -10y + -1[(-7 + 7y) + -3y + 3] Reorder the terms: -25 + 4y = 25 + -10y + -1[-7 + 3 + 7y + -3y] Combine like terms: -7 + 3 = -4 -25 + 4y = 25 + -10y + -1[-4 + 7y + -3y] Combine like terms: 7y + -3y = 4y -25 + 4y = 25 + -10y + -1[-4 + 4y] -25 + 4y = 25 + -10y + [-4 * -1 + 4y * -1] -25 + 4y = 25 + -10y + [4 + -4y] Reorder the terms: -25 + 4y = 25 + 4 + -10y + -4y Combine like terms: 25 + 4 = 29 -25 + 4y = 29 + -10y + -4y Combine like terms: -10y + -4y = -14y -25 + 4y = 29 + -14y Solving -25 + 4y = 29 + -14y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '14y' to each side of the equation. -25 + 4y + 14y = 29 + -14y + 14y Combine like terms: 4y + 14y = 18y -25 + 18y = 29 + -14y + 14y Combine like terms: -14y + 14y = 0 -25 + 18y = 29 + 0 -25 + 18y = 29 Add '25' to each side of the equation. -25 + 25 + 18y = 29 + 25 Combine like terms: -25 + 25 = 0 0 + 18y = 29 + 25 18y = 29 + 25 Combine like terms: 29 + 25 = 54 18y = 54 Divide each side by '18'. y = 3 Simplifying y = 3
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