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Simplifying 34 + -1[2 + 10y + -4(y + 5)] = -5(4y + -3) + -1[9(y + -1) + -16y + 7] Reorder the terms: 34 + -1[2 + 10y + -4(5 + y)] = -5(4y + -3) + -1[9(y + -1) + -16y + 7] 34 + -1[2 + 10y + (5 * -4 + y * -4)] = -5(4y + -3) + -1[9(y + -1) + -16y + 7] 34 + -1[2 + 10y + (-20 + -4y)] = -5(4y + -3) + -1[9(y + -1) + -16y + 7] Reorder the terms: 34 + -1[2 + -20 + 10y + -4y] = -5(4y + -3) + -1[9(y + -1) + -16y + 7] Combine like terms: 2 + -20 = -18 34 + -1[-18 + 10y + -4y] = -5(4y + -3) + -1[9(y + -1) + -16y + 7] Combine like terms: 10y + -4y = 6y 34 + -1[-18 + 6y] = -5(4y + -3) + -1[9(y + -1) + -16y + 7] 34 + [-18 * -1 + 6y * -1] = -5(4y + -3) + -1[9(y + -1) + -16y + 7] 34 + [18 + -6y] = -5(4y + -3) + -1[9(y + -1) + -16y + 7] Combine like terms: 34 + 18 = 52 52 + -6y = -5(4y + -3) + -1[9(y + -1) + -16y + 7] Reorder the terms: 52 + -6y = -5(-3 + 4y) + -1[9(y + -1) + -16y + 7] 52 + -6y = (-3 * -5 + 4y * -5) + -1[9(y + -1) + -16y + 7] 52 + -6y = (15 + -20y) + -1[9(y + -1) + -16y + 7] Reorder the terms: 52 + -6y = 15 + -20y + -1[9(-1 + y) + -16y + 7] 52 + -6y = 15 + -20y + -1[(-1 * 9 + y * 9) + -16y + 7] 52 + -6y = 15 + -20y + -1[(-9 + 9y) + -16y + 7] Reorder the terms: 52 + -6y = 15 + -20y + -1[-9 + 7 + 9y + -16y] Combine like terms: -9 + 7 = -2 52 + -6y = 15 + -20y + -1[-2 + 9y + -16y] Combine like terms: 9y + -16y = -7y 52 + -6y = 15 + -20y + -1[-2 + -7y] 52 + -6y = 15 + -20y + [-2 * -1 + -7y * -1] 52 + -6y = 15 + -20y + [2 + 7y] Reorder the terms: 52 + -6y = 15 + 2 + -20y + 7y Combine like terms: 15 + 2 = 17 52 + -6y = 17 + -20y + 7y Combine like terms: -20y + 7y = -13y 52 + -6y = 17 + -13y Solving 52 + -6y = 17 + -13y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '13y' to each side of the equation. 52 + -6y + 13y = 17 + -13y + 13y Combine like terms: -6y + 13y = 7y 52 + 7y = 17 + -13y + 13y Combine like terms: -13y + 13y = 0 52 + 7y = 17 + 0 52 + 7y = 17 Add '-52' to each side of the equation. 52 + -52 + 7y = 17 + -52 Combine like terms: 52 + -52 = 0 0 + 7y = 17 + -52 7y = 17 + -52 Combine like terms: 17 + -52 = -35 7y = -35 Divide each side by '7'. y = -5 Simplifying y = -5
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