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Simplifying 50 + -1[2 + 7y + -4(y + 2)] = -3(4y + -7) + -1[5(y + -1) + -9y + 15] Reorder the terms: 50 + -1[2 + 7y + -4(2 + y)] = -3(4y + -7) + -1[5(y + -1) + -9y + 15] 50 + -1[2 + 7y + (2 * -4 + y * -4)] = -3(4y + -7) + -1[5(y + -1) + -9y + 15] 50 + -1[2 + 7y + (-8 + -4y)] = -3(4y + -7) + -1[5(y + -1) + -9y + 15] Reorder the terms: 50 + -1[2 + -8 + 7y + -4y] = -3(4y + -7) + -1[5(y + -1) + -9y + 15] Combine like terms: 2 + -8 = -6 50 + -1[-6 + 7y + -4y] = -3(4y + -7) + -1[5(y + -1) + -9y + 15] Combine like terms: 7y + -4y = 3y 50 + -1[-6 + 3y] = -3(4y + -7) + -1[5(y + -1) + -9y + 15] 50 + [-6 * -1 + 3y * -1] = -3(4y + -7) + -1[5(y + -1) + -9y + 15] 50 + [6 + -3y] = -3(4y + -7) + -1[5(y + -1) + -9y + 15] Combine like terms: 50 + 6 = 56 56 + -3y = -3(4y + -7) + -1[5(y + -1) + -9y + 15] Reorder the terms: 56 + -3y = -3(-7 + 4y) + -1[5(y + -1) + -9y + 15] 56 + -3y = (-7 * -3 + 4y * -3) + -1[5(y + -1) + -9y + 15] 56 + -3y = (21 + -12y) + -1[5(y + -1) + -9y + 15] Reorder the terms: 56 + -3y = 21 + -12y + -1[5(-1 + y) + -9y + 15] 56 + -3y = 21 + -12y + -1[(-1 * 5 + y * 5) + -9y + 15] 56 + -3y = 21 + -12y + -1[(-5 + 5y) + -9y + 15] Reorder the terms: 56 + -3y = 21 + -12y + -1[-5 + 15 + 5y + -9y] Combine like terms: -5 + 15 = 10 56 + -3y = 21 + -12y + -1[10 + 5y + -9y] Combine like terms: 5y + -9y = -4y 56 + -3y = 21 + -12y + -1[10 + -4y] 56 + -3y = 21 + -12y + [10 * -1 + -4y * -1] 56 + -3y = 21 + -12y + [-10 + 4y] Reorder the terms: 56 + -3y = 21 + -10 + -12y + 4y Combine like terms: 21 + -10 = 11 56 + -3y = 11 + -12y + 4y Combine like terms: -12y + 4y = -8y 56 + -3y = 11 + -8y Solving 56 + -3y = 11 + -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. 56 + -3y + 8y = 11 + -8y + 8y Combine like terms: -3y + 8y = 5y 56 + 5y = 11 + -8y + 8y Combine like terms: -8y + 8y = 0 56 + 5y = 11 + 0 56 + 5y = 11 Add '-56' to each side of the equation. 56 + -56 + 5y = 11 + -56 Combine like terms: 56 + -56 = 0 0 + 5y = 11 + -56 5y = 11 + -56 Combine like terms: 11 + -56 = -45 5y = -45 Divide each side by '5'. y = -9 Simplifying y = -9
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