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Simplifying 1 + -1[2 + 6y + -4(y + 5)] = -5(2y + -7) + -1[5(y + -1) + -11y + 27] Reorder the terms: 1 + -1[2 + 6y + -4(5 + y)] = -5(2y + -7) + -1[5(y + -1) + -11y + 27] 1 + -1[2 + 6y + (5 * -4 + y * -4)] = -5(2y + -7) + -1[5(y + -1) + -11y + 27] 1 + -1[2 + 6y + (-20 + -4y)] = -5(2y + -7) + -1[5(y + -1) + -11y + 27] Reorder the terms: 1 + -1[2 + -20 + 6y + -4y] = -5(2y + -7) + -1[5(y + -1) + -11y + 27] Combine like terms: 2 + -20 = -18 1 + -1[-18 + 6y + -4y] = -5(2y + -7) + -1[5(y + -1) + -11y + 27] Combine like terms: 6y + -4y = 2y 1 + -1[-18 + 2y] = -5(2y + -7) + -1[5(y + -1) + -11y + 27] 1 + [-18 * -1 + 2y * -1] = -5(2y + -7) + -1[5(y + -1) + -11y + 27] 1 + [18 + -2y] = -5(2y + -7) + -1[5(y + -1) + -11y + 27] Combine like terms: 1 + 18 = 19 19 + -2y = -5(2y + -7) + -1[5(y + -1) + -11y + 27] Reorder the terms: 19 + -2y = -5(-7 + 2y) + -1[5(y + -1) + -11y + 27] 19 + -2y = (-7 * -5 + 2y * -5) + -1[5(y + -1) + -11y + 27] 19 + -2y = (35 + -10y) + -1[5(y + -1) + -11y + 27] Reorder the terms: 19 + -2y = 35 + -10y + -1[5(-1 + y) + -11y + 27] 19 + -2y = 35 + -10y + -1[(-1 * 5 + y * 5) + -11y + 27] 19 + -2y = 35 + -10y + -1[(-5 + 5y) + -11y + 27] Reorder the terms: 19 + -2y = 35 + -10y + -1[-5 + 27 + 5y + -11y] Combine like terms: -5 + 27 = 22 19 + -2y = 35 + -10y + -1[22 + 5y + -11y] Combine like terms: 5y + -11y = -6y 19 + -2y = 35 + -10y + -1[22 + -6y] 19 + -2y = 35 + -10y + [22 * -1 + -6y * -1] 19 + -2y = 35 + -10y + [-22 + 6y] Reorder the terms: 19 + -2y = 35 + -22 + -10y + 6y Combine like terms: 35 + -22 = 13 19 + -2y = 13 + -10y + 6y Combine like terms: -10y + 6y = -4y 19 + -2y = 13 + -4y Solving 19 + -2y = 13 + -4y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4y' to each side of the equation. 19 + -2y + 4y = 13 + -4y + 4y Combine like terms: -2y + 4y = 2y 19 + 2y = 13 + -4y + 4y Combine like terms: -4y + 4y = 0 19 + 2y = 13 + 0 19 + 2y = 13 Add '-19' to each side of the equation. 19 + -19 + 2y = 13 + -19 Combine like terms: 19 + -19 = 0 0 + 2y = 13 + -19 2y = 13 + -19 Combine like terms: 13 + -19 = -6 2y = -6 Divide each side by '2'. y = -3 Simplifying y = -3
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