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Simplifying 8(3n + 1) = 8(8n + 5) + 9 Reorder the terms: 8(1 + 3n) = 8(8n + 5) + 9 (1 * 8 + 3n * 8) = 8(8n + 5) + 9 (8 + 24n) = 8(8n + 5) + 9 Reorder the terms: 8 + 24n = 8(5 + 8n) + 9 8 + 24n = (5 * 8 + 8n * 8) + 9 8 + 24n = (40 + 64n) + 9 Reorder the terms: 8 + 24n = 40 + 9 + 64n Combine like terms: 40 + 9 = 49 8 + 24n = 49 + 64n Solving 8 + 24n = 49 + 64n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-64n' to each side of the equation. 8 + 24n + -64n = 49 + 64n + -64n Combine like terms: 24n + -64n = -40n 8 + -40n = 49 + 64n + -64n Combine like terms: 64n + -64n = 0 8 + -40n = 49 + 0 8 + -40n = 49 Add '-8' to each side of the equation. 8 + -8 + -40n = 49 + -8 Combine like terms: 8 + -8 = 0 0 + -40n = 49 + -8 -40n = 49 + -8 Combine like terms: 49 + -8 = 41 -40n = 41 Divide each side by '-40'. n = -1.025 Simplifying n = -1.025
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