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Simplifying 2[7 + -6(1 + -1n)] + 9 = -32 + 6[6(n + 1) + -3n] 2[7 + (1 * -6 + -1n * -6)] + 9 = -32 + 6[6(n + 1) + -3n] 2[7 + (-6 + 6n)] + 9 = -32 + 6[6(n + 1) + -3n] Combine like terms: 7 + -6 = 1 2[1 + 6n] + 9 = -32 + 6[6(n + 1) + -3n] [1 * 2 + 6n * 2] + 9 = -32 + 6[6(n + 1) + -3n] [2 + 12n] + 9 = -32 + 6[6(n + 1) + -3n] Reorder the terms: 2 + 9 + 12n = -32 + 6[6(n + 1) + -3n] Combine like terms: 2 + 9 = 11 11 + 12n = -32 + 6[6(n + 1) + -3n] Reorder the terms: 11 + 12n = -32 + 6[6(1 + n) + -3n] 11 + 12n = -32 + 6[(1 * 6 + n * 6) + -3n] 11 + 12n = -32 + 6[(6 + 6n) + -3n] Combine like terms: 6n + -3n = 3n 11 + 12n = -32 + 6[6 + 3n] 11 + 12n = -32 + [6 * 6 + 3n * 6] 11 + 12n = -32 + [36 + 18n] Combine like terms: -32 + 36 = 4 11 + 12n = 4 + 18n Solving 11 + 12n = 4 + 18n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-18n' to each side of the equation. 11 + 12n + -18n = 4 + 18n + -18n Combine like terms: 12n + -18n = -6n 11 + -6n = 4 + 18n + -18n Combine like terms: 18n + -18n = 0 11 + -6n = 4 + 0 11 + -6n = 4 Add '-11' to each side of the equation. 11 + -11 + -6n = 4 + -11 Combine like terms: 11 + -11 = 0 0 + -6n = 4 + -11 -6n = 4 + -11 Combine like terms: 4 + -11 = -7 -6n = -7 Divide each side by '-6'. n = 1.166666667 Simplifying n = 1.166666667
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