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Simplifying 2[7 + -5(1 + -1n)] + 7n = -11 + 3[6(n + 1) + -3n] 2[7 + (1 * -5 + -1n * -5)] + 7n = -11 + 3[6(n + 1) + -3n] 2[7 + (-5 + 5n)] + 7n = -11 + 3[6(n + 1) + -3n] Combine like terms: 7 + -5 = 2 2[2 + 5n] + 7n = -11 + 3[6(n + 1) + -3n] [2 * 2 + 5n * 2] + 7n = -11 + 3[6(n + 1) + -3n] [4 + 10n] + 7n = -11 + 3[6(n + 1) + -3n] Combine like terms: 10n + 7n = 17n 4 + 17n = -11 + 3[6(n + 1) + -3n] Reorder the terms: 4 + 17n = -11 + 3[6(1 + n) + -3n] 4 + 17n = -11 + 3[(1 * 6 + n * 6) + -3n] 4 + 17n = -11 + 3[(6 + 6n) + -3n] Combine like terms: 6n + -3n = 3n 4 + 17n = -11 + 3[6 + 3n] 4 + 17n = -11 + [6 * 3 + 3n * 3] 4 + 17n = -11 + [18 + 9n] Combine like terms: -11 + 18 = 7 4 + 17n = 7 + 9n Solving 4 + 17n = 7 + 9n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9n' to each side of the equation. 4 + 17n + -9n = 7 + 9n + -9n Combine like terms: 17n + -9n = 8n 4 + 8n = 7 + 9n + -9n Combine like terms: 9n + -9n = 0 4 + 8n = 7 + 0 4 + 8n = 7 Add '-4' to each side of the equation. 4 + -4 + 8n = 7 + -4 Combine like terms: 4 + -4 = 0 0 + 8n = 7 + -4 8n = 7 + -4 Combine like terms: 7 + -4 = 3 8n = 3 Divide each side by '8'. n = 0.375 Simplifying n = 0.375
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