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Simplifying 5(3n + 4) = 9(7n + 9) + 1 Reorder the terms: 5(4 + 3n) = 9(7n + 9) + 1 (4 * 5 + 3n * 5) = 9(7n + 9) + 1 (20 + 15n) = 9(7n + 9) + 1 Reorder the terms: 20 + 15n = 9(9 + 7n) + 1 20 + 15n = (9 * 9 + 7n * 9) + 1 20 + 15n = (81 + 63n) + 1 Reorder the terms: 20 + 15n = 81 + 1 + 63n Combine like terms: 81 + 1 = 82 20 + 15n = 82 + 63n Solving 20 + 15n = 82 + 63n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-63n' to each side of the equation. 20 + 15n + -63n = 82 + 63n + -63n Combine like terms: 15n + -63n = -48n 20 + -48n = 82 + 63n + -63n Combine like terms: 63n + -63n = 0 20 + -48n = 82 + 0 20 + -48n = 82 Add '-20' to each side of the equation. 20 + -20 + -48n = 82 + -20 Combine like terms: 20 + -20 = 0 0 + -48n = 82 + -20 -48n = 82 + -20 Combine like terms: 82 + -20 = 62 -48n = 62 Divide each side by '-48'. n = -1.291666667 Simplifying n = -1.291666667
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