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Simplifying 2[7 + -5(1 + -1n)] + 9n = -18 + 4[6(n + 1) + -3n] 2[7 + (1 * -5 + -1n * -5)] + 9n = -18 + 4[6(n + 1) + -3n] 2[7 + (-5 + 5n)] + 9n = -18 + 4[6(n + 1) + -3n] Combine like terms: 7 + -5 = 2 2[2 + 5n] + 9n = -18 + 4[6(n + 1) + -3n] [2 * 2 + 5n * 2] + 9n = -18 + 4[6(n + 1) + -3n] [4 + 10n] + 9n = -18 + 4[6(n + 1) + -3n] Combine like terms: 10n + 9n = 19n 4 + 19n = -18 + 4[6(n + 1) + -3n] Reorder the terms: 4 + 19n = -18 + 4[6(1 + n) + -3n] 4 + 19n = -18 + 4[(1 * 6 + n * 6) + -3n] 4 + 19n = -18 + 4[(6 + 6n) + -3n] Combine like terms: 6n + -3n = 3n 4 + 19n = -18 + 4[6 + 3n] 4 + 19n = -18 + [6 * 4 + 3n * 4] 4 + 19n = -18 + [24 + 12n] Combine like terms: -18 + 24 = 6 4 + 19n = 6 + 12n Solving 4 + 19n = 6 + 12n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-12n' to each side of the equation. 4 + 19n + -12n = 6 + 12n + -12n Combine like terms: 19n + -12n = 7n 4 + 7n = 6 + 12n + -12n Combine like terms: 12n + -12n = 0 4 + 7n = 6 + 0 4 + 7n = 6 Add '-4' to each side of the equation. 4 + -4 + 7n = 6 + -4 Combine like terms: 4 + -4 = 0 0 + 7n = 6 + -4 7n = 6 + -4 Combine like terms: 6 + -4 = 2 7n = 2 Divide each side by '7'. n = 0.2857142857 Simplifying n = 0.2857142857
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