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Simplifying 5(1 + 4n) + -1(1 + 8n) = 52 (1 * 5 + 4n * 5) + -1(1 + 8n) = 52 (5 + 20n) + -1(1 + 8n) = 52 5 + 20n + (1 * -1 + 8n * -1) = 52 5 + 20n + (-1 + -8n) = 52 Reorder the terms: 5 + -1 + 20n + -8n = 52 Combine like terms: 5 + -1 = 4 4 + 20n + -8n = 52 Combine like terms: 20n + -8n = 12n 4 + 12n = 52 Solving 4 + 12n = 52 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 12n = 52 + -4 Combine like terms: 4 + -4 = 0 0 + 12n = 52 + -4 12n = 52 + -4 Combine like terms: 52 + -4 = 48 12n = 48 Divide each side by '12'. n = 4 Simplifying n = 4
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