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Simplifying 5(3n + 1) = 12 + 8n Reorder the terms: 5(1 + 3n) = 12 + 8n (1 * 5 + 3n * 5) = 12 + 8n (5 + 15n) = 12 + 8n Solving 5 + 15n = 12 + 8n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8n' to each side of the equation. 5 + 15n + -8n = 12 + 8n + -8n Combine like terms: 15n + -8n = 7n 5 + 7n = 12 + 8n + -8n Combine like terms: 8n + -8n = 0 5 + 7n = 12 + 0 5 + 7n = 12 Add '-5' to each side of the equation. 5 + -5 + 7n = 12 + -5 Combine like terms: 5 + -5 = 0 0 + 7n = 12 + -5 7n = 12 + -5 Combine like terms: 12 + -5 = 7 7n = 7 Divide each side by '7'. n = 1 Simplifying n = 1
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