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Simplifying 2(3n + 1) = 8(5n + 1) + 1 Reorder the terms: 2(1 + 3n) = 8(5n + 1) + 1 (1 * 2 + 3n * 2) = 8(5n + 1) + 1 (2 + 6n) = 8(5n + 1) + 1 Reorder the terms: 2 + 6n = 8(1 + 5n) + 1 2 + 6n = (1 * 8 + 5n * 8) + 1 2 + 6n = (8 + 40n) + 1 Reorder the terms: 2 + 6n = 8 + 1 + 40n Combine like terms: 8 + 1 = 9 2 + 6n = 9 + 40n Solving 2 + 6n = 9 + 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. 2 + 6n + -40n = 9 + 40n + -40n Combine like terms: 6n + -40n = -34n 2 + -34n = 9 + 40n + -40n Combine like terms: 40n + -40n = 0 2 + -34n = 9 + 0 2 + -34n = 9 Add '-2' to each side of the equation. 2 + -2 + -34n = 9 + -2 Combine like terms: 2 + -2 = 0 0 + -34n = 9 + -2 -34n = 9 + -2 Combine like terms: 9 + -2 = 7 -34n = 7 Divide each side by '-34'. n = -0.2058823529 Simplifying n = -0.2058823529
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