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Simplifying 4(n + 9) + -9(n + -9) = 102 Reorder the terms: 4(9 + n) + -9(n + -9) = 102 (9 * 4 + n * 4) + -9(n + -9) = 102 (36 + 4n) + -9(n + -9) = 102 Reorder the terms: 36 + 4n + -9(-9 + n) = 102 36 + 4n + (-9 * -9 + n * -9) = 102 36 + 4n + (81 + -9n) = 102 Reorder the terms: 36 + 81 + 4n + -9n = 102 Combine like terms: 36 + 81 = 117 117 + 4n + -9n = 102 Combine like terms: 4n + -9n = -5n 117 + -5n = 102 Solving 117 + -5n = 102 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-117' to each side of the equation. 117 + -117 + -5n = 102 + -117 Combine like terms: 117 + -117 = 0 0 + -5n = 102 + -117 -5n = 102 + -117 Combine like terms: 102 + -117 = -15 -5n = -15 Divide each side by '-5'. n = 3 Simplifying n = 3
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