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Simplifying 9(3n + 5) = 8(5n + 1) + 6 Reorder the terms: 9(5 + 3n) = 8(5n + 1) + 6 (5 * 9 + 3n * 9) = 8(5n + 1) + 6 (45 + 27n) = 8(5n + 1) + 6 Reorder the terms: 45 + 27n = 8(1 + 5n) + 6 45 + 27n = (1 * 8 + 5n * 8) + 6 45 + 27n = (8 + 40n) + 6 Reorder the terms: 45 + 27n = 8 + 6 + 40n Combine like terms: 8 + 6 = 14 45 + 27n = 14 + 40n Solving 45 + 27n = 14 + 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. 45 + 27n + -40n = 14 + 40n + -40n Combine like terms: 27n + -40n = -13n 45 + -13n = 14 + 40n + -40n Combine like terms: 40n + -40n = 0 45 + -13n = 14 + 0 45 + -13n = 14 Add '-45' to each side of the equation. 45 + -45 + -13n = 14 + -45 Combine like terms: 45 + -45 = 0 0 + -13n = 14 + -45 -13n = 14 + -45 Combine like terms: 14 + -45 = -31 -13n = -31 Divide each side by '-13'. n = 2.384615385 Simplifying n = 2.384615385
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