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Simplifying 27 + -1[4 + 6y + -4(y + 5)] = -4(3y + -6) + -1[5(y + -1) + -11y + 10] Reorder the terms: 27 + -1[4 + 6y + -4(5 + y)] = -4(3y + -6) + -1[5(y + -1) + -11y + 10] 27 + -1[4 + 6y + (5 * -4 + y * -4)] = -4(3y + -6) + -1[5(y + -1) + -11y + 10] 27 + -1[4 + 6y + (-20 + -4y)] = -4(3y + -6) + -1[5(y + -1) + -11y + 10] Reorder the terms: 27 + -1[4 + -20 + 6y + -4y] = -4(3y + -6) + -1[5(y + -1) + -11y + 10] Combine like terms: 4 + -20 = -16 27 + -1[-16 + 6y + -4y] = -4(3y + -6) + -1[5(y + -1) + -11y + 10] Combine like terms: 6y + -4y = 2y 27 + -1[-16 + 2y] = -4(3y + -6) + -1[5(y + -1) + -11y + 10] 27 + [-16 * -1 + 2y * -1] = -4(3y + -6) + -1[5(y + -1) + -11y + 10] 27 + [16 + -2y] = -4(3y + -6) + -1[5(y + -1) + -11y + 10] Combine like terms: 27 + 16 = 43 43 + -2y = -4(3y + -6) + -1[5(y + -1) + -11y + 10] Reorder the terms: 43 + -2y = -4(-6 + 3y) + -1[5(y + -1) + -11y + 10] 43 + -2y = (-6 * -4 + 3y * -4) + -1[5(y + -1) + -11y + 10] 43 + -2y = (24 + -12y) + -1[5(y + -1) + -11y + 10] Reorder the terms: 43 + -2y = 24 + -12y + -1[5(-1 + y) + -11y + 10] 43 + -2y = 24 + -12y + -1[(-1 * 5 + y * 5) + -11y + 10] 43 + -2y = 24 + -12y + -1[(-5 + 5y) + -11y + 10] Reorder the terms: 43 + -2y = 24 + -12y + -1[-5 + 10 + 5y + -11y] Combine like terms: -5 + 10 = 5 43 + -2y = 24 + -12y + -1[5 + 5y + -11y] Combine like terms: 5y + -11y = -6y 43 + -2y = 24 + -12y + -1[5 + -6y] 43 + -2y = 24 + -12y + [5 * -1 + -6y * -1] 43 + -2y = 24 + -12y + [-5 + 6y] Reorder the terms: 43 + -2y = 24 + -5 + -12y + 6y Combine like terms: 24 + -5 = 19 43 + -2y = 19 + -12y + 6y Combine like terms: -12y + 6y = -6y 43 + -2y = 19 + -6y Solving 43 + -2y = 19 + -6y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6y' to each side of the equation. 43 + -2y + 6y = 19 + -6y + 6y Combine like terms: -2y + 6y = 4y 43 + 4y = 19 + -6y + 6y Combine like terms: -6y + 6y = 0 43 + 4y = 19 + 0 43 + 4y = 19 Add '-43' to each side of the equation. 43 + -43 + 4y = 19 + -43 Combine like terms: 43 + -43 = 0 0 + 4y = 19 + -43 4y = 19 + -43 Combine like terms: 19 + -43 = -24 4y = -24 Divide each side by '4'. y = -6 Simplifying y = -6
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