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Simplifying 43 + -1[2 + 10y + -4(y + 3)] = -5(2y + -4) + -1[7(y + -1) + -6y + 9] Reorder the terms: 43 + -1[2 + 10y + -4(3 + y)] = -5(2y + -4) + -1[7(y + -1) + -6y + 9] 43 + -1[2 + 10y + (3 * -4 + y * -4)] = -5(2y + -4) + -1[7(y + -1) + -6y + 9] 43 + -1[2 + 10y + (-12 + -4y)] = -5(2y + -4) + -1[7(y + -1) + -6y + 9] Reorder the terms: 43 + -1[2 + -12 + 10y + -4y] = -5(2y + -4) + -1[7(y + -1) + -6y + 9] Combine like terms: 2 + -12 = -10 43 + -1[-10 + 10y + -4y] = -5(2y + -4) + -1[7(y + -1) + -6y + 9] Combine like terms: 10y + -4y = 6y 43 + -1[-10 + 6y] = -5(2y + -4) + -1[7(y + -1) + -6y + 9] 43 + [-10 * -1 + 6y * -1] = -5(2y + -4) + -1[7(y + -1) + -6y + 9] 43 + [10 + -6y] = -5(2y + -4) + -1[7(y + -1) + -6y + 9] Combine like terms: 43 + 10 = 53 53 + -6y = -5(2y + -4) + -1[7(y + -1) + -6y + 9] Reorder the terms: 53 + -6y = -5(-4 + 2y) + -1[7(y + -1) + -6y + 9] 53 + -6y = (-4 * -5 + 2y * -5) + -1[7(y + -1) + -6y + 9] 53 + -6y = (20 + -10y) + -1[7(y + -1) + -6y + 9] Reorder the terms: 53 + -6y = 20 + -10y + -1[7(-1 + y) + -6y + 9] 53 + -6y = 20 + -10y + -1[(-1 * 7 + y * 7) + -6y + 9] 53 + -6y = 20 + -10y + -1[(-7 + 7y) + -6y + 9] Reorder the terms: 53 + -6y = 20 + -10y + -1[-7 + 9 + 7y + -6y] Combine like terms: -7 + 9 = 2 53 + -6y = 20 + -10y + -1[2 + 7y + -6y] Combine like terms: 7y + -6y = 1y 53 + -6y = 20 + -10y + -1[2 + 1y] 53 + -6y = 20 + -10y + [2 * -1 + 1y * -1] 53 + -6y = 20 + -10y + [-2 + -1y] Reorder the terms: 53 + -6y = 20 + -2 + -10y + -1y Combine like terms: 20 + -2 = 18 53 + -6y = 18 + -10y + -1y Combine like terms: -10y + -1y = -11y 53 + -6y = 18 + -11y Solving 53 + -6y = 18 + -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. 53 + -6y + 11y = 18 + -11y + 11y Combine like terms: -6y + 11y = 5y 53 + 5y = 18 + -11y + 11y Combine like terms: -11y + 11y = 0 53 + 5y = 18 + 0 53 + 5y = 18 Add '-53' to each side of the equation. 53 + -53 + 5y = 18 + -53 Combine like terms: 53 + -53 = 0 0 + 5y = 18 + -53 5y = 18 + -53 Combine like terms: 18 + -53 = -35 5y = -35 Divide each side by '5'. y = -7 Simplifying y = -7
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