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Simplifying 9(3n + 1) = 8(5n + 4) + 1 Reorder the terms: 9(1 + 3n) = 8(5n + 4) + 1 (1 * 9 + 3n * 9) = 8(5n + 4) + 1 (9 + 27n) = 8(5n + 4) + 1 Reorder the terms: 9 + 27n = 8(4 + 5n) + 1 9 + 27n = (4 * 8 + 5n * 8) + 1 9 + 27n = (32 + 40n) + 1 Reorder the terms: 9 + 27n = 32 + 1 + 40n Combine like terms: 32 + 1 = 33 9 + 27n = 33 + 40n Solving 9 + 27n = 33 + 40n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-40n' to each side of the equation. 9 + 27n + -40n = 33 + 40n + -40n Combine like terms: 27n + -40n = -13n 9 + -13n = 33 + 40n + -40n Combine like terms: 40n + -40n = 0 9 + -13n = 33 + 0 9 + -13n = 33 Add '-9' to each side of the equation. 9 + -9 + -13n = 33 + -9 Combine like terms: 9 + -9 = 0 0 + -13n = 33 + -9 -13n = 33 + -9 Combine like terms: 33 + -9 = 24 -13n = 24 Divide each side by '-13'. n = -1.846153846 Simplifying n = -1.846153846
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