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Simplifying 4(2n + 1) = 6(8n + 1) + 1 Reorder the terms: 4(1 + 2n) = 6(8n + 1) + 1 (1 * 4 + 2n * 4) = 6(8n + 1) + 1 (4 + 8n) = 6(8n + 1) + 1 Reorder the terms: 4 + 8n = 6(1 + 8n) + 1 4 + 8n = (1 * 6 + 8n * 6) + 1 4 + 8n = (6 + 48n) + 1 Reorder the terms: 4 + 8n = 6 + 1 + 48n Combine like terms: 6 + 1 = 7 4 + 8n = 7 + 48n Solving 4 + 8n = 7 + 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. 4 + 8n + -48n = 7 + 48n + -48n Combine like terms: 8n + -48n = -40n 4 + -40n = 7 + 48n + -48n Combine like terms: 48n + -48n = 0 4 + -40n = 7 + 0 4 + -40n = 7 Add '-4' to each side of the equation. 4 + -4 + -40n = 7 + -4 Combine like terms: 4 + -4 = 0 0 + -40n = 7 + -4 -40n = 7 + -4 Combine like terms: 7 + -4 = 3 -40n = 3 Divide each side by '-40'. n = -0.075 Simplifying n = -0.075
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