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Simplifying 4(2n + 1) = 6(7n + 9) + 1 Reorder the terms: 4(1 + 2n) = 6(7n + 9) + 1 (1 * 4 + 2n * 4) = 6(7n + 9) + 1 (4 + 8n) = 6(7n + 9) + 1 Reorder the terms: 4 + 8n = 6(9 + 7n) + 1 4 + 8n = (9 * 6 + 7n * 6) + 1 4 + 8n = (54 + 42n) + 1 Reorder the terms: 4 + 8n = 54 + 1 + 42n Combine like terms: 54 + 1 = 55 4 + 8n = 55 + 42n Solving 4 + 8n = 55 + 42n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-42n' to each side of the equation. 4 + 8n + -42n = 55 + 42n + -42n Combine like terms: 8n + -42n = -34n 4 + -34n = 55 + 42n + -42n Combine like terms: 42n + -42n = 0 4 + -34n = 55 + 0 4 + -34n = 55 Add '-4' to each side of the equation. 4 + -4 + -34n = 55 + -4 Combine like terms: 4 + -4 = 0 0 + -34n = 55 + -4 -34n = 55 + -4 Combine like terms: 55 + -4 = 51 -34n = 51 Divide each side by '-34'. n = -1.5 Simplifying n = -1.5
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