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Simplifying 3(2n + 1) = 6(5n + 9) + 7 Reorder the terms: 3(1 + 2n) = 6(5n + 9) + 7 (1 * 3 + 2n * 3) = 6(5n + 9) + 7 (3 + 6n) = 6(5n + 9) + 7 Reorder the terms: 3 + 6n = 6(9 + 5n) + 7 3 + 6n = (9 * 6 + 5n * 6) + 7 3 + 6n = (54 + 30n) + 7 Reorder the terms: 3 + 6n = 54 + 7 + 30n Combine like terms: 54 + 7 = 61 3 + 6n = 61 + 30n Solving 3 + 6n = 61 + 30n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-30n' to each side of the equation. 3 + 6n + -30n = 61 + 30n + -30n Combine like terms: 6n + -30n = -24n 3 + -24n = 61 + 30n + -30n Combine like terms: 30n + -30n = 0 3 + -24n = 61 + 0 3 + -24n = 61 Add '-3' to each side of the equation. 3 + -3 + -24n = 61 + -3 Combine like terms: 3 + -3 = 0 0 + -24n = 61 + -3 -24n = 61 + -3 Combine like terms: 61 + -3 = 58 -24n = 58 Divide each side by '-24'. n = -2.416666667 Simplifying n = -2.416666667
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