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Simplifying 5(2n + 3) = 9(3n + 5) + 1 Reorder the terms: 5(3 + 2n) = 9(3n + 5) + 1 (3 * 5 + 2n * 5) = 9(3n + 5) + 1 (15 + 10n) = 9(3n + 5) + 1 Reorder the terms: 15 + 10n = 9(5 + 3n) + 1 15 + 10n = (5 * 9 + 3n * 9) + 1 15 + 10n = (45 + 27n) + 1 Reorder the terms: 15 + 10n = 45 + 1 + 27n Combine like terms: 45 + 1 = 46 15 + 10n = 46 + 27n Solving 15 + 10n = 46 + 27n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-27n' to each side of the equation. 15 + 10n + -27n = 46 + 27n + -27n Combine like terms: 10n + -27n = -17n 15 + -17n = 46 + 27n + -27n Combine like terms: 27n + -27n = 0 15 + -17n = 46 + 0 15 + -17n = 46 Add '-15' to each side of the equation. 15 + -15 + -17n = 46 + -15 Combine like terms: 15 + -15 = 0 0 + -17n = 46 + -15 -17n = 46 + -15 Combine like terms: 46 + -15 = 31 -17n = 31 Divide each side by '-17'. n = -1.823529412 Simplifying n = -1.823529412
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