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Simplifying 5(1 + -1n) + 7(n + 1) = 8n + -5n (1 * 5 + -1n * 5) + 7(n + 1) = 8n + -5n (5 + -5n) + 7(n + 1) = 8n + -5n Reorder the terms: 5 + -5n + 7(1 + n) = 8n + -5n 5 + -5n + (1 * 7 + n * 7) = 8n + -5n 5 + -5n + (7 + 7n) = 8n + -5n Reorder the terms: 5 + 7 + -5n + 7n = 8n + -5n Combine like terms: 5 + 7 = 12 12 + -5n + 7n = 8n + -5n Combine like terms: -5n + 7n = 2n 12 + 2n = 8n + -5n Combine like terms: 8n + -5n = 3n 12 + 2n = 3n Solving 12 + 2n = 3n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3n' to each side of the equation. 12 + 2n + -3n = 3n + -3n Combine like terms: 2n + -3n = -1n 12 + -1n = 3n + -3n Combine like terms: 3n + -3n = 0 12 + -1n = 0 Add '-12' to each side of the equation. 12 + -12 + -1n = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1n = 0 + -12 -1n = 0 + -12 Combine like terms: 0 + -12 = -12 -1n = -12 Divide each side by '-1'. n = 12 Simplifying n = 12
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