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Simplifying 3(2n + 1) = 8(6n + 2) + 1 Reorder the terms: 3(1 + 2n) = 8(6n + 2) + 1 (1 * 3 + 2n * 3) = 8(6n + 2) + 1 (3 + 6n) = 8(6n + 2) + 1 Reorder the terms: 3 + 6n = 8(2 + 6n) + 1 3 + 6n = (2 * 8 + 6n * 8) + 1 3 + 6n = (16 + 48n) + 1 Reorder the terms: 3 + 6n = 16 + 1 + 48n Combine like terms: 16 + 1 = 17 3 + 6n = 17 + 48n Solving 3 + 6n = 17 + 48n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-48n' to each side of the equation. 3 + 6n + -48n = 17 + 48n + -48n Combine like terms: 6n + -48n = -42n 3 + -42n = 17 + 48n + -48n Combine like terms: 48n + -48n = 0 3 + -42n = 17 + 0 3 + -42n = 17 Add '-3' to each side of the equation. 3 + -3 + -42n = 17 + -3 Combine like terms: 3 + -3 = 0 0 + -42n = 17 + -3 -42n = 17 + -3 Combine like terms: 17 + -3 = 14 -42n = 14 Divide each side by '-42'. n = -0.3333333333 Simplifying n = -0.3333333333
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