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Simplifying 5(n + -10) + 12(n + 7) = 8n + 7n Reorder the terms: 5(-10 + n) + 12(n + 7) = 8n + 7n (-10 * 5 + n * 5) + 12(n + 7) = 8n + 7n (-50 + 5n) + 12(n + 7) = 8n + 7n Reorder the terms: -50 + 5n + 12(7 + n) = 8n + 7n -50 + 5n + (7 * 12 + n * 12) = 8n + 7n -50 + 5n + (84 + 12n) = 8n + 7n Reorder the terms: -50 + 84 + 5n + 12n = 8n + 7n Combine like terms: -50 + 84 = 34 34 + 5n + 12n = 8n + 7n Combine like terms: 5n + 12n = 17n 34 + 17n = 8n + 7n Combine like terms: 8n + 7n = 15n 34 + 17n = 15n Solving 34 + 17n = 15n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-15n' to each side of the equation. 34 + 17n + -15n = 15n + -15n Combine like terms: 17n + -15n = 2n 34 + 2n = 15n + -15n Combine like terms: 15n + -15n = 0 34 + 2n = 0 Add '-34' to each side of the equation. 34 + -34 + 2n = 0 + -34 Combine like terms: 34 + -34 = 0 0 + 2n = 0 + -34 2n = 0 + -34 Combine like terms: 0 + -34 = -34 2n = -34 Divide each side by '2'. n = -17 Simplifying n = -17
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