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Simplifying 3(2n + 3) = 8(5n + 4) + 1 Reorder the terms: 3(3 + 2n) = 8(5n + 4) + 1 (3 * 3 + 2n * 3) = 8(5n + 4) + 1 (9 + 6n) = 8(5n + 4) + 1 Reorder the terms: 9 + 6n = 8(4 + 5n) + 1 9 + 6n = (4 * 8 + 5n * 8) + 1 9 + 6n = (32 + 40n) + 1 Reorder the terms: 9 + 6n = 32 + 1 + 40n Combine like terms: 32 + 1 = 33 9 + 6n = 33 + 40n Solving 9 + 6n = 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 + 6n + -40n = 33 + 40n + -40n Combine like terms: 6n + -40n = -34n 9 + -34n = 33 + 40n + -40n Combine like terms: 40n + -40n = 0 9 + -34n = 33 + 0 9 + -34n = 33 Add '-9' to each side of the equation. 9 + -9 + -34n = 33 + -9 Combine like terms: 9 + -9 = 0 0 + -34n = 33 + -9 -34n = 33 + -9 Combine like terms: 33 + -9 = 24 -34n = 24 Divide each side by '-34'. n = -0.7058823529 Simplifying n = -0.7058823529
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