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Simplifying 2(7 + -6(1 + -1n)) + 6n = -14 + 3(6(n + 1) + -3n) 2(7 + (1 * -6 + -1n * -6)) + 6n = -14 + 3(6(n + 1) + -3n) 2(7 + (-6 + 6n)) + 6n = -14 + 3(6(n + 1) + -3n) Combine like terms: 7 + -6 = 1 2(1 + 6n) + 6n = -14 + 3(6(n + 1) + -3n) (1 * 2 + 6n * 2) + 6n = -14 + 3(6(n + 1) + -3n) (2 + 12n) + 6n = -14 + 3(6(n + 1) + -3n) Combine like terms: 12n + 6n = 18n 2 + 18n = -14 + 3(6(n + 1) + -3n) Reorder the terms: 2 + 18n = -14 + 3(6(1 + n) + -3n) 2 + 18n = -14 + 3((1 * 6 + n * 6) + -3n) 2 + 18n = -14 + 3((6 + 6n) + -3n) Combine like terms: 6n + -3n = 3n 2 + 18n = -14 + 3(6 + 3n) 2 + 18n = -14 + (6 * 3 + 3n * 3) 2 + 18n = -14 + (18 + 9n) Combine like terms: -14 + 18 = 4 2 + 18n = 4 + 9n Solving 2 + 18n = 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 + 18n + -9n = 4 + 9n + -9n Combine like terms: 18n + -9n = 9n 2 + 9n = 4 + 9n + -9n Combine like terms: 9n + -9n = 0 2 + 9n = 4 + 0 2 + 9n = 4 Add '-2' to each side of the equation. 2 + -2 + 9n = 4 + -2 Combine like terms: 2 + -2 = 0 0 + 9n = 4 + -2 9n = 4 + -2 Combine like terms: 4 + -2 = 2 9n = 2 Divide each side by '9'. n = 0.2222222222 Simplifying n = 0.2222222222
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