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Simplifying 5(2n + 3) + 4n = 2(4n + 12) + 9 Reorder the terms: 5(3 + 2n) + 4n = 2(4n + 12) + 9 (3 * 5 + 2n * 5) + 4n = 2(4n + 12) + 9 (15 + 10n) + 4n = 2(4n + 12) + 9 Combine like terms: 10n + 4n = 14n 15 + 14n = 2(4n + 12) + 9 Reorder the terms: 15 + 14n = 2(12 + 4n) + 9 15 + 14n = (12 * 2 + 4n * 2) + 9 15 + 14n = (24 + 8n) + 9 Reorder the terms: 15 + 14n = 24 + 9 + 8n Combine like terms: 24 + 9 = 33 15 + 14n = 33 + 8n Solving 15 + 14n = 33 + 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. 15 + 14n + -8n = 33 + 8n + -8n Combine like terms: 14n + -8n = 6n 15 + 6n = 33 + 8n + -8n Combine like terms: 8n + -8n = 0 15 + 6n = 33 + 0 15 + 6n = 33 Add '-15' to each side of the equation. 15 + -15 + 6n = 33 + -15 Combine like terms: 15 + -15 = 0 0 + 6n = 33 + -15 6n = 33 + -15 Combine like terms: 33 + -15 = 18 6n = 18 Divide each side by '6'. n = 3 Simplifying n = 3
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