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Simplifying 5(3n + 1) = 7(6n + 9) + 2 Reorder the terms: 5(1 + 3n) = 7(6n + 9) + 2 (1 * 5 + 3n * 5) = 7(6n + 9) + 2 (5 + 15n) = 7(6n + 9) + 2 Reorder the terms: 5 + 15n = 7(9 + 6n) + 2 5 + 15n = (9 * 7 + 6n * 7) + 2 5 + 15n = (63 + 42n) + 2 Reorder the terms: 5 + 15n = 63 + 2 + 42n Combine like terms: 63 + 2 = 65 5 + 15n = 65 + 42n Solving 5 + 15n = 65 + 42n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-42n' to each side of the equation. 5 + 15n + -42n = 65 + 42n + -42n Combine like terms: 15n + -42n = -27n 5 + -27n = 65 + 42n + -42n Combine like terms: 42n + -42n = 0 5 + -27n = 65 + 0 5 + -27n = 65 Add '-5' to each side of the equation. 5 + -5 + -27n = 65 + -5 Combine like terms: 5 + -5 = 0 0 + -27n = 65 + -5 -27n = 65 + -5 Combine like terms: 65 + -5 = 60 -27n = 60 Divide each side by '-27'. n = -2.222222222 Simplifying n = -2.222222222
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