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Simplifying 2[7 + -5(1 + -1n)] + 7n = -11 + 3[2(n + 1) + -3n] 2[7 + (1 * -5 + -1n * -5)] + 7n = -11 + 3[2(n + 1) + -3n] 2[7 + (-5 + 5n)] + 7n = -11 + 3[2(n + 1) + -3n] Combine like terms: 7 + -5 = 2 2[2 + 5n] + 7n = -11 + 3[2(n + 1) + -3n] [2 * 2 + 5n * 2] + 7n = -11 + 3[2(n + 1) + -3n] [4 + 10n] + 7n = -11 + 3[2(n + 1) + -3n] Combine like terms: 10n + 7n = 17n 4 + 17n = -11 + 3[2(n + 1) + -3n] Reorder the terms: 4 + 17n = -11 + 3[2(1 + n) + -3n] 4 + 17n = -11 + 3[(1 * 2 + n * 2) + -3n] 4 + 17n = -11 + 3[(2 + 2n) + -3n] Combine like terms: 2n + -3n = -1n 4 + 17n = -11 + 3[2 + -1n] 4 + 17n = -11 + [2 * 3 + -1n * 3] 4 + 17n = -11 + [6 + -3n] Combine like terms: -11 + 6 = -5 4 + 17n = -5 + -3n Solving 4 + 17n = -5 + -3n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3n' to each side of the equation. 4 + 17n + 3n = -5 + -3n + 3n Combine like terms: 17n + 3n = 20n 4 + 20n = -5 + -3n + 3n Combine like terms: -3n + 3n = 0 4 + 20n = -5 + 0 4 + 20n = -5 Add '-4' to each side of the equation. 4 + -4 + 20n = -5 + -4 Combine like terms: 4 + -4 = 0 0 + 20n = -5 + -4 20n = -5 + -4 Combine like terms: -5 + -4 = -9 20n = -9 Divide each side by '20'. n = -0.45 Simplifying n = -0.45
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