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Simplifying 5(2n + 1) = 6(6n + 7) + 8 Reorder the terms: 5(1 + 2n) = 6(6n + 7) + 8 (1 * 5 + 2n * 5) = 6(6n + 7) + 8 (5 + 10n) = 6(6n + 7) + 8 Reorder the terms: 5 + 10n = 6(7 + 6n) + 8 5 + 10n = (7 * 6 + 6n * 6) + 8 5 + 10n = (42 + 36n) + 8 Reorder the terms: 5 + 10n = 42 + 8 + 36n Combine like terms: 42 + 8 = 50 5 + 10n = 50 + 36n Solving 5 + 10n = 50 + 36n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-36n' to each side of the equation. 5 + 10n + -36n = 50 + 36n + -36n Combine like terms: 10n + -36n = -26n 5 + -26n = 50 + 36n + -36n Combine like terms: 36n + -36n = 0 5 + -26n = 50 + 0 5 + -26n = 50 Add '-5' to each side of the equation. 5 + -5 + -26n = 50 + -5 Combine like terms: 5 + -5 = 0 0 + -26n = 50 + -5 -26n = 50 + -5 Combine like terms: 50 + -5 = 45 -26n = 45 Divide each side by '-26'. n = -1.730769231 Simplifying n = -1.730769231
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