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Simplifying 2[7 + -6(1 + -1n)] + 8n = -14 + 3[6(n + 1) + -3n] 2[7 + (1 * -6 + -1n * -6)] + 8n = -14 + 3[6(n + 1) + -3n] 2[7 + (-6 + 6n)] + 8n = -14 + 3[6(n + 1) + -3n] Combine like terms: 7 + -6 = 1 2[1 + 6n] + 8n = -14 + 3[6(n + 1) + -3n] [1 * 2 + 6n * 2] + 8n = -14 + 3[6(n + 1) + -3n] [2 + 12n] + 8n = -14 + 3[6(n + 1) + -3n] Combine like terms: 12n + 8n = 20n 2 + 20n = -14 + 3[6(n + 1) + -3n] Reorder the terms: 2 + 20n = -14 + 3[6(1 + n) + -3n] 2 + 20n = -14 + 3[(1 * 6 + n * 6) + -3n] 2 + 20n = -14 + 3[(6 + 6n) + -3n] Combine like terms: 6n + -3n = 3n 2 + 20n = -14 + 3[6 + 3n] 2 + 20n = -14 + [6 * 3 + 3n * 3] 2 + 20n = -14 + [18 + 9n] Combine like terms: -14 + 18 = 4 2 + 20n = 4 + 9n Solving 2 + 20n = 4 + 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. 2 + 20n + -9n = 4 + 9n + -9n Combine like terms: 20n + -9n = 11n 2 + 11n = 4 + 9n + -9n Combine like terms: 9n + -9n = 0 2 + 11n = 4 + 0 2 + 11n = 4 Add '-2' to each side of the equation. 2 + -2 + 11n = 4 + -2 Combine like terms: 2 + -2 = 0 0 + 11n = 4 + -2 11n = 4 + -2 Combine like terms: 4 + -2 = 2 11n = 2 Divide each side by '11'. n = 0.1818181818 Simplifying n = 0.1818181818
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