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Simplifying -29 + -1[2 + 5y + -7(y + 2)] = -7(2y + -5) + -1[5(y + -1) + -3y + 3] Reorder the terms: -29 + -1[2 + 5y + -7(2 + y)] = -7(2y + -5) + -1[5(y + -1) + -3y + 3] -29 + -1[2 + 5y + (2 * -7 + y * -7)] = -7(2y + -5) + -1[5(y + -1) + -3y + 3] -29 + -1[2 + 5y + (-14 + -7y)] = -7(2y + -5) + -1[5(y + -1) + -3y + 3] Reorder the terms: -29 + -1[2 + -14 + 5y + -7y] = -7(2y + -5) + -1[5(y + -1) + -3y + 3] Combine like terms: 2 + -14 = -12 -29 + -1[-12 + 5y + -7y] = -7(2y + -5) + -1[5(y + -1) + -3y + 3] Combine like terms: 5y + -7y = -2y -29 + -1[-12 + -2y] = -7(2y + -5) + -1[5(y + -1) + -3y + 3] -29 + [-12 * -1 + -2y * -1] = -7(2y + -5) + -1[5(y + -1) + -3y + 3] -29 + [12 + 2y] = -7(2y + -5) + -1[5(y + -1) + -3y + 3] Combine like terms: -29 + 12 = -17 -17 + 2y = -7(2y + -5) + -1[5(y + -1) + -3y + 3] Reorder the terms: -17 + 2y = -7(-5 + 2y) + -1[5(y + -1) + -3y + 3] -17 + 2y = (-5 * -7 + 2y * -7) + -1[5(y + -1) + -3y + 3] -17 + 2y = (35 + -14y) + -1[5(y + -1) + -3y + 3] Reorder the terms: -17 + 2y = 35 + -14y + -1[5(-1 + y) + -3y + 3] -17 + 2y = 35 + -14y + -1[(-1 * 5 + y * 5) + -3y + 3] -17 + 2y = 35 + -14y + -1[(-5 + 5y) + -3y + 3] Reorder the terms: -17 + 2y = 35 + -14y + -1[-5 + 3 + 5y + -3y] Combine like terms: -5 + 3 = -2 -17 + 2y = 35 + -14y + -1[-2 + 5y + -3y] Combine like terms: 5y + -3y = 2y -17 + 2y = 35 + -14y + -1[-2 + 2y] -17 + 2y = 35 + -14y + [-2 * -1 + 2y * -1] -17 + 2y = 35 + -14y + [2 + -2y] Reorder the terms: -17 + 2y = 35 + 2 + -14y + -2y Combine like terms: 35 + 2 = 37 -17 + 2y = 37 + -14y + -2y Combine like terms: -14y + -2y = -16y -17 + 2y = 37 + -16y Solving -17 + 2y = 37 + -16y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '16y' to each side of the equation. -17 + 2y + 16y = 37 + -16y + 16y Combine like terms: 2y + 16y = 18y -17 + 18y = 37 + -16y + 16y Combine like terms: -16y + 16y = 0 -17 + 18y = 37 + 0 -17 + 18y = 37 Add '17' to each side of the equation. -17 + 17 + 18y = 37 + 17 Combine like terms: -17 + 17 = 0 0 + 18y = 37 + 17 18y = 37 + 17 Combine like terms: 37 + 17 = 54 18y = 54 Divide each side by '18'. y = 3 Simplifying y = 3
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