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Simplifying 17 + -1[3 + 7y + -3(y + 5)] = -2(5y + -7) + -1[6(y + -1) + -10y + 5] Reorder the terms: 17 + -1[3 + 7y + -3(5 + y)] = -2(5y + -7) + -1[6(y + -1) + -10y + 5] 17 + -1[3 + 7y + (5 * -3 + y * -3)] = -2(5y + -7) + -1[6(y + -1) + -10y + 5] 17 + -1[3 + 7y + (-15 + -3y)] = -2(5y + -7) + -1[6(y + -1) + -10y + 5] Reorder the terms: 17 + -1[3 + -15 + 7y + -3y] = -2(5y + -7) + -1[6(y + -1) + -10y + 5] Combine like terms: 3 + -15 = -12 17 + -1[-12 + 7y + -3y] = -2(5y + -7) + -1[6(y + -1) + -10y + 5] Combine like terms: 7y + -3y = 4y 17 + -1[-12 + 4y] = -2(5y + -7) + -1[6(y + -1) + -10y + 5] 17 + [-12 * -1 + 4y * -1] = -2(5y + -7) + -1[6(y + -1) + -10y + 5] 17 + [12 + -4y] = -2(5y + -7) + -1[6(y + -1) + -10y + 5] Combine like terms: 17 + 12 = 29 29 + -4y = -2(5y + -7) + -1[6(y + -1) + -10y + 5] Reorder the terms: 29 + -4y = -2(-7 + 5y) + -1[6(y + -1) + -10y + 5] 29 + -4y = (-7 * -2 + 5y * -2) + -1[6(y + -1) + -10y + 5] 29 + -4y = (14 + -10y) + -1[6(y + -1) + -10y + 5] Reorder the terms: 29 + -4y = 14 + -10y + -1[6(-1 + y) + -10y + 5] 29 + -4y = 14 + -10y + -1[(-1 * 6 + y * 6) + -10y + 5] 29 + -4y = 14 + -10y + -1[(-6 + 6y) + -10y + 5] Reorder the terms: 29 + -4y = 14 + -10y + -1[-6 + 5 + 6y + -10y] Combine like terms: -6 + 5 = -1 29 + -4y = 14 + -10y + -1[-1 + 6y + -10y] Combine like terms: 6y + -10y = -4y 29 + -4y = 14 + -10y + -1[-1 + -4y] 29 + -4y = 14 + -10y + [-1 * -1 + -4y * -1] 29 + -4y = 14 + -10y + [1 + 4y] Reorder the terms: 29 + -4y = 14 + 1 + -10y + 4y Combine like terms: 14 + 1 = 15 29 + -4y = 15 + -10y + 4y Combine like terms: -10y + 4y = -6y 29 + -4y = 15 + -6y Solving 29 + -4y = 15 + -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. 29 + -4y + 6y = 15 + -6y + 6y Combine like terms: -4y + 6y = 2y 29 + 2y = 15 + -6y + 6y Combine like terms: -6y + 6y = 0 29 + 2y = 15 + 0 29 + 2y = 15 Add '-29' to each side of the equation. 29 + -29 + 2y = 15 + -29 Combine like terms: 29 + -29 = 0 0 + 2y = 15 + -29 2y = 15 + -29 Combine like terms: 15 + -29 = -14 2y = -14 Divide each side by '2'. y = -7 Simplifying y = -7
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