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Simplifying 5(3n + 2) = 9(9n + 5) + 1 Reorder the terms: 5(2 + 3n) = 9(9n + 5) + 1 (2 * 5 + 3n * 5) = 9(9n + 5) + 1 (10 + 15n) = 9(9n + 5) + 1 Reorder the terms: 10 + 15n = 9(5 + 9n) + 1 10 + 15n = (5 * 9 + 9n * 9) + 1 10 + 15n = (45 + 81n) + 1 Reorder the terms: 10 + 15n = 45 + 1 + 81n Combine like terms: 45 + 1 = 46 10 + 15n = 46 + 81n Solving 10 + 15n = 46 + 81n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-81n' to each side of the equation. 10 + 15n + -81n = 46 + 81n + -81n Combine like terms: 15n + -81n = -66n 10 + -66n = 46 + 81n + -81n Combine like terms: 81n + -81n = 0 10 + -66n = 46 + 0 10 + -66n = 46 Add '-10' to each side of the equation. 10 + -10 + -66n = 46 + -10 Combine like terms: 10 + -10 = 0 0 + -66n = 46 + -10 -66n = 46 + -10 Combine like terms: 46 + -10 = 36 -66n = 36 Divide each side by '-66'. n = -0.5454545455 Simplifying n = -0.5454545455
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