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Simplifying 43 + -1[3 + 8y + -4(y + 3)] = -2(5y + -6) + -1[9(y + -1) + -6y + 5] Reorder the terms: 43 + -1[3 + 8y + -4(3 + y)] = -2(5y + -6) + -1[9(y + -1) + -6y + 5] 43 + -1[3 + 8y + (3 * -4 + y * -4)] = -2(5y + -6) + -1[9(y + -1) + -6y + 5] 43 + -1[3 + 8y + (-12 + -4y)] = -2(5y + -6) + -1[9(y + -1) + -6y + 5] Reorder the terms: 43 + -1[3 + -12 + 8y + -4y] = -2(5y + -6) + -1[9(y + -1) + -6y + 5] Combine like terms: 3 + -12 = -9 43 + -1[-9 + 8y + -4y] = -2(5y + -6) + -1[9(y + -1) + -6y + 5] Combine like terms: 8y + -4y = 4y 43 + -1[-9 + 4y] = -2(5y + -6) + -1[9(y + -1) + -6y + 5] 43 + [-9 * -1 + 4y * -1] = -2(5y + -6) + -1[9(y + -1) + -6y + 5] 43 + [9 + -4y] = -2(5y + -6) + -1[9(y + -1) + -6y + 5] Combine like terms: 43 + 9 = 52 52 + -4y = -2(5y + -6) + -1[9(y + -1) + -6y + 5] Reorder the terms: 52 + -4y = -2(-6 + 5y) + -1[9(y + -1) + -6y + 5] 52 + -4y = (-6 * -2 + 5y * -2) + -1[9(y + -1) + -6y + 5] 52 + -4y = (12 + -10y) + -1[9(y + -1) + -6y + 5] Reorder the terms: 52 + -4y = 12 + -10y + -1[9(-1 + y) + -6y + 5] 52 + -4y = 12 + -10y + -1[(-1 * 9 + y * 9) + -6y + 5] 52 + -4y = 12 + -10y + -1[(-9 + 9y) + -6y + 5] Reorder the terms: 52 + -4y = 12 + -10y + -1[-9 + 5 + 9y + -6y] Combine like terms: -9 + 5 = -4 52 + -4y = 12 + -10y + -1[-4 + 9y + -6y] Combine like terms: 9y + -6y = 3y 52 + -4y = 12 + -10y + -1[-4 + 3y] 52 + -4y = 12 + -10y + [-4 * -1 + 3y * -1] 52 + -4y = 12 + -10y + [4 + -3y] Reorder the terms: 52 + -4y = 12 + 4 + -10y + -3y Combine like terms: 12 + 4 = 16 52 + -4y = 16 + -10y + -3y Combine like terms: -10y + -3y = -13y 52 + -4y = 16 + -13y Solving 52 + -4y = 16 + -13y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '13y' to each side of the equation. 52 + -4y + 13y = 16 + -13y + 13y Combine like terms: -4y + 13y = 9y 52 + 9y = 16 + -13y + 13y Combine like terms: -13y + 13y = 0 52 + 9y = 16 + 0 52 + 9y = 16 Add '-52' to each side of the equation. 52 + -52 + 9y = 16 + -52 Combine like terms: 52 + -52 = 0 0 + 9y = 16 + -52 9y = 16 + -52 Combine like terms: 16 + -52 = -36 9y = -36 Divide each side by '9'. y = -4 Simplifying y = -4
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