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Simplifying 33 + -1[2 + 7y + -3(y + 4)] = -3(3y + -7) + -1[5(y + -1) + -3y + 11] Reorder the terms: 33 + -1[2 + 7y + -3(4 + y)] = -3(3y + -7) + -1[5(y + -1) + -3y + 11] 33 + -1[2 + 7y + (4 * -3 + y * -3)] = -3(3y + -7) + -1[5(y + -1) + -3y + 11] 33 + -1[2 + 7y + (-12 + -3y)] = -3(3y + -7) + -1[5(y + -1) + -3y + 11] Reorder the terms: 33 + -1[2 + -12 + 7y + -3y] = -3(3y + -7) + -1[5(y + -1) + -3y + 11] Combine like terms: 2 + -12 = -10 33 + -1[-10 + 7y + -3y] = -3(3y + -7) + -1[5(y + -1) + -3y + 11] Combine like terms: 7y + -3y = 4y 33 + -1[-10 + 4y] = -3(3y + -7) + -1[5(y + -1) + -3y + 11] 33 + [-10 * -1 + 4y * -1] = -3(3y + -7) + -1[5(y + -1) + -3y + 11] 33 + [10 + -4y] = -3(3y + -7) + -1[5(y + -1) + -3y + 11] Combine like terms: 33 + 10 = 43 43 + -4y = -3(3y + -7) + -1[5(y + -1) + -3y + 11] Reorder the terms: 43 + -4y = -3(-7 + 3y) + -1[5(y + -1) + -3y + 11] 43 + -4y = (-7 * -3 + 3y * -3) + -1[5(y + -1) + -3y + 11] 43 + -4y = (21 + -9y) + -1[5(y + -1) + -3y + 11] Reorder the terms: 43 + -4y = 21 + -9y + -1[5(-1 + y) + -3y + 11] 43 + -4y = 21 + -9y + -1[(-1 * 5 + y * 5) + -3y + 11] 43 + -4y = 21 + -9y + -1[(-5 + 5y) + -3y + 11] Reorder the terms: 43 + -4y = 21 + -9y + -1[-5 + 11 + 5y + -3y] Combine like terms: -5 + 11 = 6 43 + -4y = 21 + -9y + -1[6 + 5y + -3y] Combine like terms: 5y + -3y = 2y 43 + -4y = 21 + -9y + -1[6 + 2y] 43 + -4y = 21 + -9y + [6 * -1 + 2y * -1] 43 + -4y = 21 + -9y + [-6 + -2y] Reorder the terms: 43 + -4y = 21 + -6 + -9y + -2y Combine like terms: 21 + -6 = 15 43 + -4y = 15 + -9y + -2y Combine like terms: -9y + -2y = -11y 43 + -4y = 15 + -11y Solving 43 + -4y = 15 + -11y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11y' to each side of the equation. 43 + -4y + 11y = 15 + -11y + 11y Combine like terms: -4y + 11y = 7y 43 + 7y = 15 + -11y + 11y Combine like terms: -11y + 11y = 0 43 + 7y = 15 + 0 43 + 7y = 15 Add '-43' to each side of the equation. 43 + -43 + 7y = 15 + -43 Combine like terms: 43 + -43 = 0 0 + 7y = 15 + -43 7y = 15 + -43 Combine like terms: 15 + -43 = -28 7y = -28 Divide each side by '7'. y = -4 Simplifying y = -4
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