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Simplifying 36 + -1[5 + 7y + -4(y + 3)] = -5(2y + -3) + -1[6(y + -1) + -8y + 8] Reorder the terms: 36 + -1[5 + 7y + -4(3 + y)] = -5(2y + -3) + -1[6(y + -1) + -8y + 8] 36 + -1[5 + 7y + (3 * -4 + y * -4)] = -5(2y + -3) + -1[6(y + -1) + -8y + 8] 36 + -1[5 + 7y + (-12 + -4y)] = -5(2y + -3) + -1[6(y + -1) + -8y + 8] Reorder the terms: 36 + -1[5 + -12 + 7y + -4y] = -5(2y + -3) + -1[6(y + -1) + -8y + 8] Combine like terms: 5 + -12 = -7 36 + -1[-7 + 7y + -4y] = -5(2y + -3) + -1[6(y + -1) + -8y + 8] Combine like terms: 7y + -4y = 3y 36 + -1[-7 + 3y] = -5(2y + -3) + -1[6(y + -1) + -8y + 8] 36 + [-7 * -1 + 3y * -1] = -5(2y + -3) + -1[6(y + -1) + -8y + 8] 36 + [7 + -3y] = -5(2y + -3) + -1[6(y + -1) + -8y + 8] Combine like terms: 36 + 7 = 43 43 + -3y = -5(2y + -3) + -1[6(y + -1) + -8y + 8] Reorder the terms: 43 + -3y = -5(-3 + 2y) + -1[6(y + -1) + -8y + 8] 43 + -3y = (-3 * -5 + 2y * -5) + -1[6(y + -1) + -8y + 8] 43 + -3y = (15 + -10y) + -1[6(y + -1) + -8y + 8] Reorder the terms: 43 + -3y = 15 + -10y + -1[6(-1 + y) + -8y + 8] 43 + -3y = 15 + -10y + -1[(-1 * 6 + y * 6) + -8y + 8] 43 + -3y = 15 + -10y + -1[(-6 + 6y) + -8y + 8] Reorder the terms: 43 + -3y = 15 + -10y + -1[-6 + 8 + 6y + -8y] Combine like terms: -6 + 8 = 2 43 + -3y = 15 + -10y + -1[2 + 6y + -8y] Combine like terms: 6y + -8y = -2y 43 + -3y = 15 + -10y + -1[2 + -2y] 43 + -3y = 15 + -10y + [2 * -1 + -2y * -1] 43 + -3y = 15 + -10y + [-2 + 2y] Reorder the terms: 43 + -3y = 15 + -2 + -10y + 2y Combine like terms: 15 + -2 = 13 43 + -3y = 13 + -10y + 2y Combine like terms: -10y + 2y = -8y 43 + -3y = 13 + -8y Solving 43 + -3y = 13 + -8y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8y' to each side of the equation. 43 + -3y + 8y = 13 + -8y + 8y Combine like terms: -3y + 8y = 5y 43 + 5y = 13 + -8y + 8y Combine like terms: -8y + 8y = 0 43 + 5y = 13 + 0 43 + 5y = 13 Add '-43' to each side of the equation. 43 + -43 + 5y = 13 + -43 Combine like terms: 43 + -43 = 0 0 + 5y = 13 + -43 5y = 13 + -43 Combine like terms: 13 + -43 = -30 5y = -30 Divide each side by '5'. y = -6 Simplifying y = -6
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