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Simplifying 9(3n + 1) = 9(5n + 8) + 1 Reorder the terms: 9(1 + 3n) = 9(5n + 8) + 1 (1 * 9 + 3n * 9) = 9(5n + 8) + 1 (9 + 27n) = 9(5n + 8) + 1 Reorder the terms: 9 + 27n = 9(8 + 5n) + 1 9 + 27n = (8 * 9 + 5n * 9) + 1 9 + 27n = (72 + 45n) + 1 Reorder the terms: 9 + 27n = 72 + 1 + 45n Combine like terms: 72 + 1 = 73 9 + 27n = 73 + 45n Solving 9 + 27n = 73 + 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. 9 + 27n + -45n = 73 + 45n + -45n Combine like terms: 27n + -45n = -18n 9 + -18n = 73 + 45n + -45n Combine like terms: 45n + -45n = 0 9 + -18n = 73 + 0 9 + -18n = 73 Add '-9' to each side of the equation. 9 + -9 + -18n = 73 + -9 Combine like terms: 9 + -9 = 0 0 + -18n = 73 + -9 -18n = 73 + -9 Combine like terms: 73 + -9 = 64 -18n = 64 Divide each side by '-18'. n = -3.555555556 Simplifying n = -3.555555556
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