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Simplifying 8 + -1(6 + -6n) + 9 = -2 + 12(n + 1) 8 + (6 * -1 + -6n * -1) + 9 = -2 + 12(n + 1) 8 + (-6 + 6n) + 9 = -2 + 12(n + 1) Reorder the terms: 8 + -6 + 9 + 6n = -2 + 12(n + 1) Combine like terms: 8 + -6 = 2 2 + 9 + 6n = -2 + 12(n + 1) Combine like terms: 2 + 9 = 11 11 + 6n = -2 + 12(n + 1) Reorder the terms: 11 + 6n = -2 + 12(1 + n) 11 + 6n = -2 + (1 * 12 + n * 12) 11 + 6n = -2 + (12 + 12n) Combine like terms: -2 + 12 = 10 11 + 6n = 10 + 12n Solving 11 + 6n = 10 + 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. 11 + 6n + -12n = 10 + 12n + -12n Combine like terms: 6n + -12n = -6n 11 + -6n = 10 + 12n + -12n Combine like terms: 12n + -12n = 0 11 + -6n = 10 + 0 11 + -6n = 10 Add '-11' to each side of the equation. 11 + -11 + -6n = 10 + -11 Combine like terms: 11 + -11 = 0 0 + -6n = 10 + -11 -6n = 10 + -11 Combine like terms: 10 + -11 = -1 -6n = -1 Divide each side by '-6'. n = 0.1666666667 Simplifying n = 0.1666666667
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