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Simplifying 30 + -1[4 + 7y + -4(y + 4)] = -2(3y + -4) + -1[9(y + -1) + -8y + 3] Reorder the terms: 30 + -1[4 + 7y + -4(4 + y)] = -2(3y + -4) + -1[9(y + -1) + -8y + 3] 30 + -1[4 + 7y + (4 * -4 + y * -4)] = -2(3y + -4) + -1[9(y + -1) + -8y + 3] 30 + -1[4 + 7y + (-16 + -4y)] = -2(3y + -4) + -1[9(y + -1) + -8y + 3] Reorder the terms: 30 + -1[4 + -16 + 7y + -4y] = -2(3y + -4) + -1[9(y + -1) + -8y + 3] Combine like terms: 4 + -16 = -12 30 + -1[-12 + 7y + -4y] = -2(3y + -4) + -1[9(y + -1) + -8y + 3] Combine like terms: 7y + -4y = 3y 30 + -1[-12 + 3y] = -2(3y + -4) + -1[9(y + -1) + -8y + 3] 30 + [-12 * -1 + 3y * -1] = -2(3y + -4) + -1[9(y + -1) + -8y + 3] 30 + [12 + -3y] = -2(3y + -4) + -1[9(y + -1) + -8y + 3] Combine like terms: 30 + 12 = 42 42 + -3y = -2(3y + -4) + -1[9(y + -1) + -8y + 3] Reorder the terms: 42 + -3y = -2(-4 + 3y) + -1[9(y + -1) + -8y + 3] 42 + -3y = (-4 * -2 + 3y * -2) + -1[9(y + -1) + -8y + 3] 42 + -3y = (8 + -6y) + -1[9(y + -1) + -8y + 3] Reorder the terms: 42 + -3y = 8 + -6y + -1[9(-1 + y) + -8y + 3] 42 + -3y = 8 + -6y + -1[(-1 * 9 + y * 9) + -8y + 3] 42 + -3y = 8 + -6y + -1[(-9 + 9y) + -8y + 3] Reorder the terms: 42 + -3y = 8 + -6y + -1[-9 + 3 + 9y + -8y] Combine like terms: -9 + 3 = -6 42 + -3y = 8 + -6y + -1[-6 + 9y + -8y] Combine like terms: 9y + -8y = 1y 42 + -3y = 8 + -6y + -1[-6 + 1y] 42 + -3y = 8 + -6y + [-6 * -1 + 1y * -1] 42 + -3y = 8 + -6y + [6 + -1y] Reorder the terms: 42 + -3y = 8 + 6 + -6y + -1y Combine like terms: 8 + 6 = 14 42 + -3y = 14 + -6y + -1y Combine like terms: -6y + -1y = -7y 42 + -3y = 14 + -7y Solving 42 + -3y = 14 + -7y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7y' to each side of the equation. 42 + -3y + 7y = 14 + -7y + 7y Combine like terms: -3y + 7y = 4y 42 + 4y = 14 + -7y + 7y Combine like terms: -7y + 7y = 0 42 + 4y = 14 + 0 42 + 4y = 14 Add '-42' to each side of the equation. 42 + -42 + 4y = 14 + -42 Combine like terms: 42 + -42 = 0 0 + 4y = 14 + -42 4y = 14 + -42 Combine like terms: 14 + -42 = -28 4y = -28 Divide each side by '4'. y = -7 Simplifying y = -7
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