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Simplifying 3(2n + 1) = 8(3n + 7) + 1 Reorder the terms: 3(1 + 2n) = 8(3n + 7) + 1 (1 * 3 + 2n * 3) = 8(3n + 7) + 1 (3 + 6n) = 8(3n + 7) + 1 Reorder the terms: 3 + 6n = 8(7 + 3n) + 1 3 + 6n = (7 * 8 + 3n * 8) + 1 3 + 6n = (56 + 24n) + 1 Reorder the terms: 3 + 6n = 56 + 1 + 24n Combine like terms: 56 + 1 = 57 3 + 6n = 57 + 24n Solving 3 + 6n = 57 + 24n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-24n' to each side of the equation. 3 + 6n + -24n = 57 + 24n + -24n Combine like terms: 6n + -24n = -18n 3 + -18n = 57 + 24n + -24n Combine like terms: 24n + -24n = 0 3 + -18n = 57 + 0 3 + -18n = 57 Add '-3' to each side of the equation. 3 + -3 + -18n = 57 + -3 Combine like terms: 3 + -3 = 0 0 + -18n = 57 + -3 -18n = 57 + -3 Combine like terms: 57 + -3 = 54 -18n = 54 Divide each side by '-18'. n = -3 Simplifying n = -3
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