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Simplifying 14 + -1[1 + 5y + -2(y + 5)] = -4(2y + -6) + -1[5(y + -1) + -7y + 18] Reorder the terms: 14 + -1[1 + 5y + -2(5 + y)] = -4(2y + -6) + -1[5(y + -1) + -7y + 18] 14 + -1[1 + 5y + (5 * -2 + y * -2)] = -4(2y + -6) + -1[5(y + -1) + -7y + 18] 14 + -1[1 + 5y + (-10 + -2y)] = -4(2y + -6) + -1[5(y + -1) + -7y + 18] Reorder the terms: 14 + -1[1 + -10 + 5y + -2y] = -4(2y + -6) + -1[5(y + -1) + -7y + 18] Combine like terms: 1 + -10 = -9 14 + -1[-9 + 5y + -2y] = -4(2y + -6) + -1[5(y + -1) + -7y + 18] Combine like terms: 5y + -2y = 3y 14 + -1[-9 + 3y] = -4(2y + -6) + -1[5(y + -1) + -7y + 18] 14 + [-9 * -1 + 3y * -1] = -4(2y + -6) + -1[5(y + -1) + -7y + 18] 14 + [9 + -3y] = -4(2y + -6) + -1[5(y + -1) + -7y + 18] Combine like terms: 14 + 9 = 23 23 + -3y = -4(2y + -6) + -1[5(y + -1) + -7y + 18] Reorder the terms: 23 + -3y = -4(-6 + 2y) + -1[5(y + -1) + -7y + 18] 23 + -3y = (-6 * -4 + 2y * -4) + -1[5(y + -1) + -7y + 18] 23 + -3y = (24 + -8y) + -1[5(y + -1) + -7y + 18] Reorder the terms: 23 + -3y = 24 + -8y + -1[5(-1 + y) + -7y + 18] 23 + -3y = 24 + -8y + -1[(-1 * 5 + y * 5) + -7y + 18] 23 + -3y = 24 + -8y + -1[(-5 + 5y) + -7y + 18] Reorder the terms: 23 + -3y = 24 + -8y + -1[-5 + 18 + 5y + -7y] Combine like terms: -5 + 18 = 13 23 + -3y = 24 + -8y + -1[13 + 5y + -7y] Combine like terms: 5y + -7y = -2y 23 + -3y = 24 + -8y + -1[13 + -2y] 23 + -3y = 24 + -8y + [13 * -1 + -2y * -1] 23 + -3y = 24 + -8y + [-13 + 2y] Reorder the terms: 23 + -3y = 24 + -13 + -8y + 2y Combine like terms: 24 + -13 = 11 23 + -3y = 11 + -8y + 2y Combine like terms: -8y + 2y = -6y 23 + -3y = 11 + -6y Solving 23 + -3y = 11 + -6y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6y' to each side of the equation. 23 + -3y + 6y = 11 + -6y + 6y Combine like terms: -3y + 6y = 3y 23 + 3y = 11 + -6y + 6y Combine like terms: -6y + 6y = 0 23 + 3y = 11 + 0 23 + 3y = 11 Add '-23' to each side of the equation. 23 + -23 + 3y = 11 + -23 Combine like terms: 23 + -23 = 0 0 + 3y = 11 + -23 3y = 11 + -23 Combine like terms: 11 + -23 = -12 3y = -12 Divide each side by '3'. y = -4 Simplifying y = -4
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