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Simplifying 4(1 + 3n) = 8(n + 5) (1 * 4 + 3n * 4) = 8(n + 5) (4 + 12n) = 8(n + 5) Reorder the terms: 4 + 12n = 8(5 + n) 4 + 12n = (5 * 8 + n * 8) 4 + 12n = (40 + 8n) Solving 4 + 12n = 40 + 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. 4 + 12n + -8n = 40 + 8n + -8n Combine like terms: 12n + -8n = 4n 4 + 4n = 40 + 8n + -8n Combine like terms: 8n + -8n = 0 4 + 4n = 40 + 0 4 + 4n = 40 Add '-4' to each side of the equation. 4 + -4 + 4n = 40 + -4 Combine like terms: 4 + -4 = 0 0 + 4n = 40 + -4 4n = 40 + -4 Combine like terms: 40 + -4 = 36 4n = 36 Divide each side by '4'. n = 9 Simplifying n = 9
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