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Simplifying 33 + -1[3 + 6y + -4(y + 3)] = -4(5y + -5) + -1[5(y + -1) + -19y + 11] Reorder the terms: 33 + -1[3 + 6y + -4(3 + y)] = -4(5y + -5) + -1[5(y + -1) + -19y + 11] 33 + -1[3 + 6y + (3 * -4 + y * -4)] = -4(5y + -5) + -1[5(y + -1) + -19y + 11] 33 + -1[3 + 6y + (-12 + -4y)] = -4(5y + -5) + -1[5(y + -1) + -19y + 11] Reorder the terms: 33 + -1[3 + -12 + 6y + -4y] = -4(5y + -5) + -1[5(y + -1) + -19y + 11] Combine like terms: 3 + -12 = -9 33 + -1[-9 + 6y + -4y] = -4(5y + -5) + -1[5(y + -1) + -19y + 11] Combine like terms: 6y + -4y = 2y 33 + -1[-9 + 2y] = -4(5y + -5) + -1[5(y + -1) + -19y + 11] 33 + [-9 * -1 + 2y * -1] = -4(5y + -5) + -1[5(y + -1) + -19y + 11] 33 + [9 + -2y] = -4(5y + -5) + -1[5(y + -1) + -19y + 11] Combine like terms: 33 + 9 = 42 42 + -2y = -4(5y + -5) + -1[5(y + -1) + -19y + 11] Reorder the terms: 42 + -2y = -4(-5 + 5y) + -1[5(y + -1) + -19y + 11] 42 + -2y = (-5 * -4 + 5y * -4) + -1[5(y + -1) + -19y + 11] 42 + -2y = (20 + -20y) + -1[5(y + -1) + -19y + 11] Reorder the terms: 42 + -2y = 20 + -20y + -1[5(-1 + y) + -19y + 11] 42 + -2y = 20 + -20y + -1[(-1 * 5 + y * 5) + -19y + 11] 42 + -2y = 20 + -20y + -1[(-5 + 5y) + -19y + 11] Reorder the terms: 42 + -2y = 20 + -20y + -1[-5 + 11 + 5y + -19y] Combine like terms: -5 + 11 = 6 42 + -2y = 20 + -20y + -1[6 + 5y + -19y] Combine like terms: 5y + -19y = -14y 42 + -2y = 20 + -20y + -1[6 + -14y] 42 + -2y = 20 + -20y + [6 * -1 + -14y * -1] 42 + -2y = 20 + -20y + [-6 + 14y] Reorder the terms: 42 + -2y = 20 + -6 + -20y + 14y Combine like terms: 20 + -6 = 14 42 + -2y = 14 + -20y + 14y Combine like terms: -20y + 14y = -6y 42 + -2y = 14 + -6y Solving 42 + -2y = 14 + -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. 42 + -2y + 6y = 14 + -6y + 6y Combine like terms: -2y + 6y = 4y 42 + 4y = 14 + -6y + 6y Combine like terms: -6y + 6y = 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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