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Simplifying 8(3n + 1) = 8(5n + 6) + 9 Reorder the terms: 8(1 + 3n) = 8(5n + 6) + 9 (1 * 8 + 3n * 8) = 8(5n + 6) + 9 (8 + 24n) = 8(5n + 6) + 9 Reorder the terms: 8 + 24n = 8(6 + 5n) + 9 8 + 24n = (6 * 8 + 5n * 8) + 9 8 + 24n = (48 + 40n) + 9 Reorder the terms: 8 + 24n = 48 + 9 + 40n Combine like terms: 48 + 9 = 57 8 + 24n = 57 + 40n Solving 8 + 24n = 57 + 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. 8 + 24n + -40n = 57 + 40n + -40n Combine like terms: 24n + -40n = -16n 8 + -16n = 57 + 40n + -40n Combine like terms: 40n + -40n = 0 8 + -16n = 57 + 0 8 + -16n = 57 Add '-8' to each side of the equation. 8 + -8 + -16n = 57 + -8 Combine like terms: 8 + -8 = 0 0 + -16n = 57 + -8 -16n = 57 + -8 Combine like terms: 57 + -8 = 49 -16n = 49 Divide each side by '-16'. n = -3.0625 Simplifying n = -3.0625
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