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Simplifying 3(3n + 1) = 9(5n + 3) + 3 Reorder the terms: 3(1 + 3n) = 9(5n + 3) + 3 (1 * 3 + 3n * 3) = 9(5n + 3) + 3 (3 + 9n) = 9(5n + 3) + 3 Reorder the terms: 3 + 9n = 9(3 + 5n) + 3 3 + 9n = (3 * 9 + 5n * 9) + 3 3 + 9n = (27 + 45n) + 3 Reorder the terms: 3 + 9n = 27 + 3 + 45n Combine like terms: 27 + 3 = 30 3 + 9n = 30 + 45n Solving 3 + 9n = 30 + 45n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-45n' to each side of the equation. 3 + 9n + -45n = 30 + 45n + -45n Combine like terms: 9n + -45n = -36n 3 + -36n = 30 + 45n + -45n Combine like terms: 45n + -45n = 0 3 + -36n = 30 + 0 3 + -36n = 30 Add '-3' to each side of the equation. 3 + -3 + -36n = 30 + -3 Combine like terms: 3 + -3 = 0 0 + -36n = 30 + -3 -36n = 30 + -3 Combine like terms: 30 + -3 = 27 -36n = 27 Divide each side by '-36'. n = -0.75 Simplifying n = -0.75
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