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Simplifying 1 + n + 6n = 5(1 + 3n) + -7(n + 2) Combine like terms: n + 6n = 7n 1 + 7n = 5(1 + 3n) + -7(n + 2) 1 + 7n = (1 * 5 + 3n * 5) + -7(n + 2) 1 + 7n = (5 + 15n) + -7(n + 2) Reorder the terms: 1 + 7n = 5 + 15n + -7(2 + n) 1 + 7n = 5 + 15n + (2 * -7 + n * -7) 1 + 7n = 5 + 15n + (-14 + -7n) Reorder the terms: 1 + 7n = 5 + -14 + 15n + -7n Combine like terms: 5 + -14 = -9 1 + 7n = -9 + 15n + -7n Combine like terms: 15n + -7n = 8n 1 + 7n = -9 + 8n Solving 1 + 7n = -9 + 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. 1 + 7n + -8n = -9 + 8n + -8n Combine like terms: 7n + -8n = -1n 1 + -1n = -9 + 8n + -8n Combine like terms: 8n + -8n = 0 1 + -1n = -9 + 0 1 + -1n = -9 Add '-1' to each side of the equation. 1 + -1 + -1n = -9 + -1 Combine like terms: 1 + -1 = 0 0 + -1n = -9 + -1 -1n = -9 + -1 Combine like terms: -9 + -1 = -10 -1n = -10 Divide each side by '-1'. n = 10 Simplifying n = 10
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