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Simplifying 3(n + 9) + 11(n + -12) = 3n + 1 + 2n + 2 Reorder the terms: 3(9 + n) + 11(n + -12) = 3n + 1 + 2n + 2 (9 * 3 + n * 3) + 11(n + -12) = 3n + 1 + 2n + 2 (27 + 3n) + 11(n + -12) = 3n + 1 + 2n + 2 Reorder the terms: 27 + 3n + 11(-12 + n) = 3n + 1 + 2n + 2 27 + 3n + (-12 * 11 + n * 11) = 3n + 1 + 2n + 2 27 + 3n + (-132 + 11n) = 3n + 1 + 2n + 2 Reorder the terms: 27 + -132 + 3n + 11n = 3n + 1 + 2n + 2 Combine like terms: 27 + -132 = -105 -105 + 3n + 11n = 3n + 1 + 2n + 2 Combine like terms: 3n + 11n = 14n -105 + 14n = 3n + 1 + 2n + 2 Reorder the terms: -105 + 14n = 1 + 2 + 3n + 2n Combine like terms: 1 + 2 = 3 -105 + 14n = 3 + 3n + 2n Combine like terms: 3n + 2n = 5n -105 + 14n = 3 + 5n Solving -105 + 14n = 3 + 5n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5n' to each side of the equation. -105 + 14n + -5n = 3 + 5n + -5n Combine like terms: 14n + -5n = 9n -105 + 9n = 3 + 5n + -5n Combine like terms: 5n + -5n = 0 -105 + 9n = 3 + 0 -105 + 9n = 3 Add '105' to each side of the equation. -105 + 105 + 9n = 3 + 105 Combine like terms: -105 + 105 = 0 0 + 9n = 3 + 105 9n = 3 + 105 Combine like terms: 3 + 105 = 108 9n = 108 Divide each side by '9'. n = 12 Simplifying n = 12
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