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Simplifying 2(3n + 5) = 7(5n + 7) + 1 Reorder the terms: 2(5 + 3n) = 7(5n + 7) + 1 (5 * 2 + 3n * 2) = 7(5n + 7) + 1 (10 + 6n) = 7(5n + 7) + 1 Reorder the terms: 10 + 6n = 7(7 + 5n) + 1 10 + 6n = (7 * 7 + 5n * 7) + 1 10 + 6n = (49 + 35n) + 1 Reorder the terms: 10 + 6n = 49 + 1 + 35n Combine like terms: 49 + 1 = 50 10 + 6n = 50 + 35n Solving 10 + 6n = 50 + 35n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-35n' to each side of the equation. 10 + 6n + -35n = 50 + 35n + -35n Combine like terms: 6n + -35n = -29n 10 + -29n = 50 + 35n + -35n Combine like terms: 35n + -35n = 0 10 + -29n = 50 + 0 10 + -29n = 50 Add '-10' to each side of the equation. 10 + -10 + -29n = 50 + -10 Combine like terms: 10 + -10 = 0 0 + -29n = 50 + -10 -29n = 50 + -10 Combine like terms: 50 + -10 = 40 -29n = 40 Divide each side by '-29'. n = -1.379310345 Simplifying n = -1.379310345
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