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Simplifying 5(2n + 1) = 8(8n + 5) + 1 Reorder the terms: 5(1 + 2n) = 8(8n + 5) + 1 (1 * 5 + 2n * 5) = 8(8n + 5) + 1 (5 + 10n) = 8(8n + 5) + 1 Reorder the terms: 5 + 10n = 8(5 + 8n) + 1 5 + 10n = (5 * 8 + 8n * 8) + 1 5 + 10n = (40 + 64n) + 1 Reorder the terms: 5 + 10n = 40 + 1 + 64n Combine like terms: 40 + 1 = 41 5 + 10n = 41 + 64n Solving 5 + 10n = 41 + 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. 5 + 10n + -64n = 41 + 64n + -64n Combine like terms: 10n + -64n = -54n 5 + -54n = 41 + 64n + -64n Combine like terms: 64n + -64n = 0 5 + -54n = 41 + 0 5 + -54n = 41 Add '-5' to each side of the equation. 5 + -5 + -54n = 41 + -5 Combine like terms: 5 + -5 = 0 0 + -54n = 41 + -5 -54n = 41 + -5 Combine like terms: 41 + -5 = 36 -54n = 36 Divide each side by '-54'. n = -0.6666666667 Simplifying n = -0.6666666667
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