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Simplifying 22 + -1[5 + 5y + -2(y + 4)] = -5(2y + -3) + -1[6(y + -1) + -7y + 8] Reorder the terms: 22 + -1[5 + 5y + -2(4 + y)] = -5(2y + -3) + -1[6(y + -1) + -7y + 8] 22 + -1[5 + 5y + (4 * -2 + y * -2)] = -5(2y + -3) + -1[6(y + -1) + -7y + 8] 22 + -1[5 + 5y + (-8 + -2y)] = -5(2y + -3) + -1[6(y + -1) + -7y + 8] Reorder the terms: 22 + -1[5 + -8 + 5y + -2y] = -5(2y + -3) + -1[6(y + -1) + -7y + 8] Combine like terms: 5 + -8 = -3 22 + -1[-3 + 5y + -2y] = -5(2y + -3) + -1[6(y + -1) + -7y + 8] Combine like terms: 5y + -2y = 3y 22 + -1[-3 + 3y] = -5(2y + -3) + -1[6(y + -1) + -7y + 8] 22 + [-3 * -1 + 3y * -1] = -5(2y + -3) + -1[6(y + -1) + -7y + 8] 22 + [3 + -3y] = -5(2y + -3) + -1[6(y + -1) + -7y + 8] Combine like terms: 22 + 3 = 25 25 + -3y = -5(2y + -3) + -1[6(y + -1) + -7y + 8] Reorder the terms: 25 + -3y = -5(-3 + 2y) + -1[6(y + -1) + -7y + 8] 25 + -3y = (-3 * -5 + 2y * -5) + -1[6(y + -1) + -7y + 8] 25 + -3y = (15 + -10y) + -1[6(y + -1) + -7y + 8] Reorder the terms: 25 + -3y = 15 + -10y + -1[6(-1 + y) + -7y + 8] 25 + -3y = 15 + -10y + -1[(-1 * 6 + y * 6) + -7y + 8] 25 + -3y = 15 + -10y + -1[(-6 + 6y) + -7y + 8] Reorder the terms: 25 + -3y = 15 + -10y + -1[-6 + 8 + 6y + -7y] Combine like terms: -6 + 8 = 2 25 + -3y = 15 + -10y + -1[2 + 6y + -7y] Combine like terms: 6y + -7y = -1y 25 + -3y = 15 + -10y + -1[2 + -1y] 25 + -3y = 15 + -10y + [2 * -1 + -1y * -1] 25 + -3y = 15 + -10y + [-2 + 1y] Reorder the terms: 25 + -3y = 15 + -2 + -10y + 1y Combine like terms: 15 + -2 = 13 25 + -3y = 13 + -10y + 1y Combine like terms: -10y + 1y = -9y 25 + -3y = 13 + -9y Solving 25 + -3y = 13 + -9y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9y' to each side of the equation. 25 + -3y + 9y = 13 + -9y + 9y Combine like terms: -3y + 9y = 6y 25 + 6y = 13 + -9y + 9y Combine like terms: -9y + 9y = 0 25 + 6y = 13 + 0 25 + 6y = 13 Add '-25' to each side of the equation. 25 + -25 + 6y = 13 + -25 Combine like terms: 25 + -25 = 0 0 + 6y = 13 + -25 6y = 13 + -25 Combine like terms: 13 + -25 = -12 6y = -12 Divide each side by '6'. y = -2 Simplifying y = -2
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