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Simplifying 29 + -1[5 + 5y + -2(y + 3)] = 4(4y + -7) + -1[6(y + -1) + -13y + 16] Reorder the terms: 29 + -1[5 + 5y + -2(3 + y)] = 4(4y + -7) + -1[6(y + -1) + -13y + 16] 29 + -1[5 + 5y + (3 * -2 + y * -2)] = 4(4y + -7) + -1[6(y + -1) + -13y + 16] 29 + -1[5 + 5y + (-6 + -2y)] = 4(4y + -7) + -1[6(y + -1) + -13y + 16] Reorder the terms: 29 + -1[5 + -6 + 5y + -2y] = 4(4y + -7) + -1[6(y + -1) + -13y + 16] Combine like terms: 5 + -6 = -1 29 + -1[-1 + 5y + -2y] = 4(4y + -7) + -1[6(y + -1) + -13y + 16] Combine like terms: 5y + -2y = 3y 29 + -1[-1 + 3y] = 4(4y + -7) + -1[6(y + -1) + -13y + 16] 29 + [-1 * -1 + 3y * -1] = 4(4y + -7) + -1[6(y + -1) + -13y + 16] 29 + [1 + -3y] = 4(4y + -7) + -1[6(y + -1) + -13y + 16] Combine like terms: 29 + 1 = 30 30 + -3y = 4(4y + -7) + -1[6(y + -1) + -13y + 16] Reorder the terms: 30 + -3y = 4(-7 + 4y) + -1[6(y + -1) + -13y + 16] 30 + -3y = (-7 * 4 + 4y * 4) + -1[6(y + -1) + -13y + 16] 30 + -3y = (-28 + 16y) + -1[6(y + -1) + -13y + 16] Reorder the terms: 30 + -3y = -28 + 16y + -1[6(-1 + y) + -13y + 16] 30 + -3y = -28 + 16y + -1[(-1 * 6 + y * 6) + -13y + 16] 30 + -3y = -28 + 16y + -1[(-6 + 6y) + -13y + 16] Reorder the terms: 30 + -3y = -28 + 16y + -1[-6 + 16 + 6y + -13y] Combine like terms: -6 + 16 = 10 30 + -3y = -28 + 16y + -1[10 + 6y + -13y] Combine like terms: 6y + -13y = -7y 30 + -3y = -28 + 16y + -1[10 + -7y] 30 + -3y = -28 + 16y + [10 * -1 + -7y * -1] 30 + -3y = -28 + 16y + [-10 + 7y] Reorder the terms: 30 + -3y = -28 + -10 + 16y + 7y Combine like terms: -28 + -10 = -38 30 + -3y = -38 + 16y + 7y Combine like terms: 16y + 7y = 23y 30 + -3y = -38 + 23y Solving 30 + -3y = -38 + 23y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-23y' to each side of the equation. 30 + -3y + -23y = -38 + 23y + -23y Combine like terms: -3y + -23y = -26y 30 + -26y = -38 + 23y + -23y Combine like terms: 23y + -23y = 0 30 + -26y = -38 + 0 30 + -26y = -38 Add '-30' to each side of the equation. 30 + -30 + -26y = -38 + -30 Combine like terms: 30 + -30 = 0 0 + -26y = -38 + -30 -26y = -38 + -30 Combine like terms: -38 + -30 = -68 -26y = -68 Divide each side by '-26'. y = 2.615384615 Simplifying y = 2.615384615
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