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Simplifying 40 + -1[4 + 7y + -2(y + 5)] = -3(3y + -7) + -1[5(y + -1) + -3y + 10] Reorder the terms: 40 + -1[4 + 7y + -2(5 + y)] = -3(3y + -7) + -1[5(y + -1) + -3y + 10] 40 + -1[4 + 7y + (5 * -2 + y * -2)] = -3(3y + -7) + -1[5(y + -1) + -3y + 10] 40 + -1[4 + 7y + (-10 + -2y)] = -3(3y + -7) + -1[5(y + -1) + -3y + 10] Reorder the terms: 40 + -1[4 + -10 + 7y + -2y] = -3(3y + -7) + -1[5(y + -1) + -3y + 10] Combine like terms: 4 + -10 = -6 40 + -1[-6 + 7y + -2y] = -3(3y + -7) + -1[5(y + -1) + -3y + 10] Combine like terms: 7y + -2y = 5y 40 + -1[-6 + 5y] = -3(3y + -7) + -1[5(y + -1) + -3y + 10] 40 + [-6 * -1 + 5y * -1] = -3(3y + -7) + -1[5(y + -1) + -3y + 10] 40 + [6 + -5y] = -3(3y + -7) + -1[5(y + -1) + -3y + 10] Combine like terms: 40 + 6 = 46 46 + -5y = -3(3y + -7) + -1[5(y + -1) + -3y + 10] Reorder the terms: 46 + -5y = -3(-7 + 3y) + -1[5(y + -1) + -3y + 10] 46 + -5y = (-7 * -3 + 3y * -3) + -1[5(y + -1) + -3y + 10] 46 + -5y = (21 + -9y) + -1[5(y + -1) + -3y + 10] Reorder the terms: 46 + -5y = 21 + -9y + -1[5(-1 + y) + -3y + 10] 46 + -5y = 21 + -9y + -1[(-1 * 5 + y * 5) + -3y + 10] 46 + -5y = 21 + -9y + -1[(-5 + 5y) + -3y + 10] Reorder the terms: 46 + -5y = 21 + -9y + -1[-5 + 10 + 5y + -3y] Combine like terms: -5 + 10 = 5 46 + -5y = 21 + -9y + -1[5 + 5y + -3y] Combine like terms: 5y + -3y = 2y 46 + -5y = 21 + -9y + -1[5 + 2y] 46 + -5y = 21 + -9y + [5 * -1 + 2y * -1] 46 + -5y = 21 + -9y + [-5 + -2y] Reorder the terms: 46 + -5y = 21 + -5 + -9y + -2y Combine like terms: 21 + -5 = 16 46 + -5y = 16 + -9y + -2y Combine like terms: -9y + -2y = -11y 46 + -5y = 16 + -11y Solving 46 + -5y = 16 + -11y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11y' to each side of the equation. 46 + -5y + 11y = 16 + -11y + 11y Combine like terms: -5y + 11y = 6y 46 + 6y = 16 + -11y + 11y Combine like terms: -11y + 11y = 0 46 + 6y = 16 + 0 46 + 6y = 16 Add '-46' to each side of the equation. 46 + -46 + 6y = 16 + -46 Combine like terms: 46 + -46 = 0 0 + 6y = 16 + -46 6y = 16 + -46 Combine like terms: 16 + -46 = -30 6y = -30 Divide each side by '6'. y = -5 Simplifying y = -5
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