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Simplifying 27 + -1[3 + 7y + -3(y + 4)] = -5(2y + -5) + -1[8(y + -1) + -11y + 21] Reorder the terms: 27 + -1[3 + 7y + -3(4 + y)] = -5(2y + -5) + -1[8(y + -1) + -11y + 21] 27 + -1[3 + 7y + (4 * -3 + y * -3)] = -5(2y + -5) + -1[8(y + -1) + -11y + 21] 27 + -1[3 + 7y + (-12 + -3y)] = -5(2y + -5) + -1[8(y + -1) + -11y + 21] Reorder the terms: 27 + -1[3 + -12 + 7y + -3y] = -5(2y + -5) + -1[8(y + -1) + -11y + 21] Combine like terms: 3 + -12 = -9 27 + -1[-9 + 7y + -3y] = -5(2y + -5) + -1[8(y + -1) + -11y + 21] Combine like terms: 7y + -3y = 4y 27 + -1[-9 + 4y] = -5(2y + -5) + -1[8(y + -1) + -11y + 21] 27 + [-9 * -1 + 4y * -1] = -5(2y + -5) + -1[8(y + -1) + -11y + 21] 27 + [9 + -4y] = -5(2y + -5) + -1[8(y + -1) + -11y + 21] Combine like terms: 27 + 9 = 36 36 + -4y = -5(2y + -5) + -1[8(y + -1) + -11y + 21] Reorder the terms: 36 + -4y = -5(-5 + 2y) + -1[8(y + -1) + -11y + 21] 36 + -4y = (-5 * -5 + 2y * -5) + -1[8(y + -1) + -11y + 21] 36 + -4y = (25 + -10y) + -1[8(y + -1) + -11y + 21] Reorder the terms: 36 + -4y = 25 + -10y + -1[8(-1 + y) + -11y + 21] 36 + -4y = 25 + -10y + -1[(-1 * 8 + y * 8) + -11y + 21] 36 + -4y = 25 + -10y + -1[(-8 + 8y) + -11y + 21] Reorder the terms: 36 + -4y = 25 + -10y + -1[-8 + 21 + 8y + -11y] Combine like terms: -8 + 21 = 13 36 + -4y = 25 + -10y + -1[13 + 8y + -11y] Combine like terms: 8y + -11y = -3y 36 + -4y = 25 + -10y + -1[13 + -3y] 36 + -4y = 25 + -10y + [13 * -1 + -3y * -1] 36 + -4y = 25 + -10y + [-13 + 3y] Reorder the terms: 36 + -4y = 25 + -13 + -10y + 3y Combine like terms: 25 + -13 = 12 36 + -4y = 12 + -10y + 3y Combine like terms: -10y + 3y = -7y 36 + -4y = 12 + -7y Solving 36 + -4y = 12 + -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. 36 + -4y + 7y = 12 + -7y + 7y Combine like terms: -4y + 7y = 3y 36 + 3y = 12 + -7y + 7y Combine like terms: -7y + 7y = 0 36 + 3y = 12 + 0 36 + 3y = 12 Add '-36' to each side of the equation. 36 + -36 + 3y = 12 + -36 Combine like terms: 36 + -36 = 0 0 + 3y = 12 + -36 3y = 12 + -36 Combine like terms: 12 + -36 = -24 3y = -24 Divide each side by '3'. y = -8 Simplifying y = -8
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