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Simplifying 2(3n + 1) = 9(5n + 2) + 1 Reorder the terms: 2(1 + 3n) = 9(5n + 2) + 1 (1 * 2 + 3n * 2) = 9(5n + 2) + 1 (2 + 6n) = 9(5n + 2) + 1 Reorder the terms: 2 + 6n = 9(2 + 5n) + 1 2 + 6n = (2 * 9 + 5n * 9) + 1 2 + 6n = (18 + 45n) + 1 Reorder the terms: 2 + 6n = 18 + 1 + 45n Combine like terms: 18 + 1 = 19 2 + 6n = 19 + 45n Solving 2 + 6n = 19 + 45n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-45n' to each side of the equation. 2 + 6n + -45n = 19 + 45n + -45n Combine like terms: 6n + -45n = -39n 2 + -39n = 19 + 45n + -45n Combine like terms: 45n + -45n = 0 2 + -39n = 19 + 0 2 + -39n = 19 Add '-2' to each side of the equation. 2 + -2 + -39n = 19 + -2 Combine like terms: 2 + -2 = 0 0 + -39n = 19 + -2 -39n = 19 + -2 Combine like terms: 19 + -2 = 17 -39n = 17 Divide each side by '-39'. n = -0.4358974359 Simplifying n = -0.4358974359
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