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Simplifying n + n + 1 + n + 2 + n + 3 + n + 4 = -65 Reorder the terms: 1 + 2 + 3 + 4 + n + n + n + n + n = -65 Combine like terms: 1 + 2 = 3 3 + 3 + 4 + n + n + n + n + n = -65 Combine like terms: 3 + 3 = 6 6 + 4 + n + n + n + n + n = -65 Combine like terms: 6 + 4 = 10 10 + n + n + n + n + n = -65 Combine like terms: n + n = 2n 10 + 2n + n + n + n = -65 Combine like terms: 2n + n = 3n 10 + 3n + n + n = -65 Combine like terms: 3n + n = 4n 10 + 4n + n = -65 Combine like terms: 4n + n = 5n 10 + 5n = -65 Solving 10 + 5n = -65 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 5n = -65 + -10 Combine like terms: 10 + -10 = 0 0 + 5n = -65 + -10 5n = -65 + -10 Combine like terms: -65 + -10 = -75 5n = -75 Divide each side by '5'. n = -15 Simplifying n = -15
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