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Simplifying 7(n + 5) + -2(n + -4) = n + -3 + 6 + -4n Reorder the terms: 7(5 + n) + -2(n + -4) = n + -3 + 6 + -4n (5 * 7 + n * 7) + -2(n + -4) = n + -3 + 6 + -4n (35 + 7n) + -2(n + -4) = n + -3 + 6 + -4n Reorder the terms: 35 + 7n + -2(-4 + n) = n + -3 + 6 + -4n 35 + 7n + (-4 * -2 + n * -2) = n + -3 + 6 + -4n 35 + 7n + (8 + -2n) = n + -3 + 6 + -4n Reorder the terms: 35 + 8 + 7n + -2n = n + -3 + 6 + -4n Combine like terms: 35 + 8 = 43 43 + 7n + -2n = n + -3 + 6 + -4n Combine like terms: 7n + -2n = 5n 43 + 5n = n + -3 + 6 + -4n Reorder the terms: 43 + 5n = -3 + 6 + n + -4n Combine like terms: -3 + 6 = 3 43 + 5n = 3 + n + -4n Combine like terms: n + -4n = -3n 43 + 5n = 3 + -3n Solving 43 + 5n = 3 + -3n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '3n' to each side of the equation. 43 + 5n + 3n = 3 + -3n + 3n Combine like terms: 5n + 3n = 8n 43 + 8n = 3 + -3n + 3n Combine like terms: -3n + 3n = 0 43 + 8n = 3 + 0 43 + 8n = 3 Add '-43' to each side of the equation. 43 + -43 + 8n = 3 + -43 Combine like terms: 43 + -43 = 0 0 + 8n = 3 + -43 8n = 3 + -43 Combine like terms: 3 + -43 = -40 8n = -40 Divide each side by '8'. n = -5 Simplifying n = -5
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