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Simplifying 43 + -1[2 + 6y + -4(y + 4)] = -2(4y + -6) + -1[9(y + -1) + -8y + 6] Reorder the terms: 43 + -1[2 + 6y + -4(4 + y)] = -2(4y + -6) + -1[9(y + -1) + -8y + 6] 43 + -1[2 + 6y + (4 * -4 + y * -4)] = -2(4y + -6) + -1[9(y + -1) + -8y + 6] 43 + -1[2 + 6y + (-16 + -4y)] = -2(4y + -6) + -1[9(y + -1) + -8y + 6] Reorder the terms: 43 + -1[2 + -16 + 6y + -4y] = -2(4y + -6) + -1[9(y + -1) + -8y + 6] Combine like terms: 2 + -16 = -14 43 + -1[-14 + 6y + -4y] = -2(4y + -6) + -1[9(y + -1) + -8y + 6] Combine like terms: 6y + -4y = 2y 43 + -1[-14 + 2y] = -2(4y + -6) + -1[9(y + -1) + -8y + 6] 43 + [-14 * -1 + 2y * -1] = -2(4y + -6) + -1[9(y + -1) + -8y + 6] 43 + [14 + -2y] = -2(4y + -6) + -1[9(y + -1) + -8y + 6] Combine like terms: 43 + 14 = 57 57 + -2y = -2(4y + -6) + -1[9(y + -1) + -8y + 6] Reorder the terms: 57 + -2y = -2(-6 + 4y) + -1[9(y + -1) + -8y + 6] 57 + -2y = (-6 * -2 + 4y * -2) + -1[9(y + -1) + -8y + 6] 57 + -2y = (12 + -8y) + -1[9(y + -1) + -8y + 6] Reorder the terms: 57 + -2y = 12 + -8y + -1[9(-1 + y) + -8y + 6] 57 + -2y = 12 + -8y + -1[(-1 * 9 + y * 9) + -8y + 6] 57 + -2y = 12 + -8y + -1[(-9 + 9y) + -8y + 6] Reorder the terms: 57 + -2y = 12 + -8y + -1[-9 + 6 + 9y + -8y] Combine like terms: -9 + 6 = -3 57 + -2y = 12 + -8y + -1[-3 + 9y + -8y] Combine like terms: 9y + -8y = 1y 57 + -2y = 12 + -8y + -1[-3 + 1y] 57 + -2y = 12 + -8y + [-3 * -1 + 1y * -1] 57 + -2y = 12 + -8y + [3 + -1y] Reorder the terms: 57 + -2y = 12 + 3 + -8y + -1y Combine like terms: 12 + 3 = 15 57 + -2y = 15 + -8y + -1y Combine like terms: -8y + -1y = -9y 57 + -2y = 15 + -9y Solving 57 + -2y = 15 + -9y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9y' to each side of the equation. 57 + -2y + 9y = 15 + -9y + 9y Combine like terms: -2y + 9y = 7y 57 + 7y = 15 + -9y + 9y Combine like terms: -9y + 9y = 0 57 + 7y = 15 + 0 57 + 7y = 15 Add '-57' to each side of the equation. 57 + -57 + 7y = 15 + -57 Combine like terms: 57 + -57 = 0 0 + 7y = 15 + -57 7y = 15 + -57 Combine like terms: 15 + -57 = -42 7y = -42 Divide each side by '7'. y = -6 Simplifying y = -6
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