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Simplifying 2[7 + -5(1 + -1n)] + 7n = 6 + 2[6(n + 1) + -3n] 2[7 + (1 * -5 + -1n * -5)] + 7n = 6 + 2[6(n + 1) + -3n] 2[7 + (-5 + 5n)] + 7n = 6 + 2[6(n + 1) + -3n] Combine like terms: 7 + -5 = 2 2[2 + 5n] + 7n = 6 + 2[6(n + 1) + -3n] [2 * 2 + 5n * 2] + 7n = 6 + 2[6(n + 1) + -3n] [4 + 10n] + 7n = 6 + 2[6(n + 1) + -3n] Combine like terms: 10n + 7n = 17n 4 + 17n = 6 + 2[6(n + 1) + -3n] Reorder the terms: 4 + 17n = 6 + 2[6(1 + n) + -3n] 4 + 17n = 6 + 2[(1 * 6 + n * 6) + -3n] 4 + 17n = 6 + 2[(6 + 6n) + -3n] Combine like terms: 6n + -3n = 3n 4 + 17n = 6 + 2[6 + 3n] 4 + 17n = 6 + [6 * 2 + 3n * 2] 4 + 17n = 6 + [12 + 6n] Combine like terms: 6 + 12 = 18 4 + 17n = 18 + 6n Solving 4 + 17n = 18 + 6n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6n' to each side of the equation. 4 + 17n + -6n = 18 + 6n + -6n Combine like terms: 17n + -6n = 11n 4 + 11n = 18 + 6n + -6n Combine like terms: 6n + -6n = 0 4 + 11n = 18 + 0 4 + 11n = 18 Add '-4' to each side of the equation. 4 + -4 + 11n = 18 + -4 Combine like terms: 4 + -4 = 0 0 + 11n = 18 + -4 11n = 18 + -4 Combine like terms: 18 + -4 = 14 11n = 14 Divide each side by '11'. n = 1.272727273 Simplifying n = 1.272727273
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