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Simplifying 47 + -1[4 + 8y + -3(y + 3)] = -5(2y + -5) + -1[5(y + -1) + -6y + 14] Reorder the terms: 47 + -1[4 + 8y + -3(3 + y)] = -5(2y + -5) + -1[5(y + -1) + -6y + 14] 47 + -1[4 + 8y + (3 * -3 + y * -3)] = -5(2y + -5) + -1[5(y + -1) + -6y + 14] 47 + -1[4 + 8y + (-9 + -3y)] = -5(2y + -5) + -1[5(y + -1) + -6y + 14] Reorder the terms: 47 + -1[4 + -9 + 8y + -3y] = -5(2y + -5) + -1[5(y + -1) + -6y + 14] Combine like terms: 4 + -9 = -5 47 + -1[-5 + 8y + -3y] = -5(2y + -5) + -1[5(y + -1) + -6y + 14] Combine like terms: 8y + -3y = 5y 47 + -1[-5 + 5y] = -5(2y + -5) + -1[5(y + -1) + -6y + 14] 47 + [-5 * -1 + 5y * -1] = -5(2y + -5) + -1[5(y + -1) + -6y + 14] 47 + [5 + -5y] = -5(2y + -5) + -1[5(y + -1) + -6y + 14] Combine like terms: 47 + 5 = 52 52 + -5y = -5(2y + -5) + -1[5(y + -1) + -6y + 14] Reorder the terms: 52 + -5y = -5(-5 + 2y) + -1[5(y + -1) + -6y + 14] 52 + -5y = (-5 * -5 + 2y * -5) + -1[5(y + -1) + -6y + 14] 52 + -5y = (25 + -10y) + -1[5(y + -1) + -6y + 14] Reorder the terms: 52 + -5y = 25 + -10y + -1[5(-1 + y) + -6y + 14] 52 + -5y = 25 + -10y + -1[(-1 * 5 + y * 5) + -6y + 14] 52 + -5y = 25 + -10y + -1[(-5 + 5y) + -6y + 14] Reorder the terms: 52 + -5y = 25 + -10y + -1[-5 + 14 + 5y + -6y] Combine like terms: -5 + 14 = 9 52 + -5y = 25 + -10y + -1[9 + 5y + -6y] Combine like terms: 5y + -6y = -1y 52 + -5y = 25 + -10y + -1[9 + -1y] 52 + -5y = 25 + -10y + [9 * -1 + -1y * -1] 52 + -5y = 25 + -10y + [-9 + 1y] Reorder the terms: 52 + -5y = 25 + -9 + -10y + 1y Combine like terms: 25 + -9 = 16 52 + -5y = 16 + -10y + 1y Combine like terms: -10y + 1y = -9y 52 + -5y = 16 + -9y Solving 52 + -5y = 16 + -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. 52 + -5y + 9y = 16 + -9y + 9y Combine like terms: -5y + 9y = 4y 52 + 4y = 16 + -9y + 9y Combine like terms: -9y + 9y = 0 52 + 4y = 16 + 0 52 + 4y = 16 Add '-52' to each side of the equation. 52 + -52 + 4y = 16 + -52 Combine like terms: 52 + -52 = 0 0 + 4y = 16 + -52 4y = 16 + -52 Combine like terms: 16 + -52 = -36 4y = -36 Divide each side by '4'. y = -9 Simplifying y = -9
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