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