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Simplifying 5(1 + 6n) = 5 + 12(7n + 9) (1 * 5 + 6n * 5) = 5 + 12(7n + 9) (5 + 30n) = 5 + 12(7n + 9) Reorder the terms: 5 + 30n = 5 + 12(9 + 7n) 5 + 30n = 5 + (9 * 12 + 7n * 12) 5 + 30n = 5 + (108 + 84n) Combine like terms: 5 + 108 = 113 5 + 30n = 113 + 84n Solving 5 + 30n = 113 + 84n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-84n' to each side of the equation. 5 + 30n + -84n = 113 + 84n + -84n Combine like terms: 30n + -84n = -54n 5 + -54n = 113 + 84n + -84n Combine like terms: 84n + -84n = 0 5 + -54n = 113 + 0 5 + -54n = 113 Add '-5' to each side of the equation. 5 + -5 + -54n = 113 + -5 Combine like terms: 5 + -5 = 0 0 + -54n = 113 + -5 -54n = 113 + -5 Combine like terms: 113 + -5 = 108 -54n = 108 Divide each side by '-54'. n = -2 Simplifying n = -2
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