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Simplifying 7(1 + 3n) + -5(1 + -4n) = 43 (1 * 7 + 3n * 7) + -5(1 + -4n) = 43 (7 + 21n) + -5(1 + -4n) = 43 7 + 21n + (1 * -5 + -4n * -5) = 43 7 + 21n + (-5 + 20n) = 43 Reorder the terms: 7 + -5 + 21n + 20n = 43 Combine like terms: 7 + -5 = 2 2 + 21n + 20n = 43 Combine like terms: 21n + 20n = 41n 2 + 41n = 43 Solving 2 + 41n = 43 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 41n = 43 + -2 Combine like terms: 2 + -2 = 0 0 + 41n = 43 + -2 41n = 43 + -2 Combine like terms: 43 + -2 = 41 41n = 41 Divide each side by '41'. n = 1 Simplifying n = 1
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