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Simplifying 5(2n + 1) = 6(8n + 9) + 3 Reorder the terms: 5(1 + 2n) = 6(8n + 9) + 3 (1 * 5 + 2n * 5) = 6(8n + 9) + 3 (5 + 10n) = 6(8n + 9) + 3 Reorder the terms: 5 + 10n = 6(9 + 8n) + 3 5 + 10n = (9 * 6 + 8n * 6) + 3 5 + 10n = (54 + 48n) + 3 Reorder the terms: 5 + 10n = 54 + 3 + 48n Combine like terms: 54 + 3 = 57 5 + 10n = 57 + 48n Solving 5 + 10n = 57 + 48n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-48n' to each side of the equation. 5 + 10n + -48n = 57 + 48n + -48n Combine like terms: 10n + -48n = -38n 5 + -38n = 57 + 48n + -48n Combine like terms: 48n + -48n = 0 5 + -38n = 57 + 0 5 + -38n = 57 Add '-5' to each side of the equation. 5 + -5 + -38n = 57 + -5 Combine like terms: 5 + -5 = 0 0 + -38n = 57 + -5 -38n = 57 + -5 Combine like terms: 57 + -5 = 52 -38n = 52 Divide each side by '-38'. n = -1.368421053 Simplifying n = -1.368421053
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