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Simplifying 91 = 4(1 + 9n) + 7(1 + -4n) 91 = (1 * 4 + 9n * 4) + 7(1 + -4n) 91 = (4 + 36n) + 7(1 + -4n) 91 = 4 + 36n + (1 * 7 + -4n * 7) 91 = 4 + 36n + (7 + -28n) Reorder the terms: 91 = 4 + 7 + 36n + -28n Combine like terms: 4 + 7 = 11 91 = 11 + 36n + -28n Combine like terms: 36n + -28n = 8n 91 = 11 + 8n Solving 91 = 11 + 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. 91 + -8n = 11 + 8n + -8n Combine like terms: 8n + -8n = 0 91 + -8n = 11 + 0 91 + -8n = 11 Add '-91' to each side of the equation. 91 + -91 + -8n = 11 + -91 Combine like terms: 91 + -91 = 0 0 + -8n = 11 + -91 -8n = 11 + -91 Combine like terms: 11 + -91 = -80 -8n = -80 Divide each side by '-8'. n = 10 Simplifying n = 10
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