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Simplifying 4(2n + 1) = 8(9n + 1) + 2 Reorder the terms: 4(1 + 2n) = 8(9n + 1) + 2 (1 * 4 + 2n * 4) = 8(9n + 1) + 2 (4 + 8n) = 8(9n + 1) + 2 Reorder the terms: 4 + 8n = 8(1 + 9n) + 2 4 + 8n = (1 * 8 + 9n * 8) + 2 4 + 8n = (8 + 72n) + 2 Reorder the terms: 4 + 8n = 8 + 2 + 72n Combine like terms: 8 + 2 = 10 4 + 8n = 10 + 72n Solving 4 + 8n = 10 + 72n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-72n' to each side of the equation. 4 + 8n + -72n = 10 + 72n + -72n Combine like terms: 8n + -72n = -64n 4 + -64n = 10 + 72n + -72n Combine like terms: 72n + -72n = 0 4 + -64n = 10 + 0 4 + -64n = 10 Add '-4' to each side of the equation. 4 + -4 + -64n = 10 + -4 Combine like terms: 4 + -4 = 0 0 + -64n = 10 + -4 -64n = 10 + -4 Combine like terms: 10 + -4 = 6 -64n = 6 Divide each side by '-64'. n = -0.09375 Simplifying n = -0.09375
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