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Simplifying 3(3n + 4) = 7(4n + 8) + 1 Reorder the terms: 3(4 + 3n) = 7(4n + 8) + 1 (4 * 3 + 3n * 3) = 7(4n + 8) + 1 (12 + 9n) = 7(4n + 8) + 1 Reorder the terms: 12 + 9n = 7(8 + 4n) + 1 12 + 9n = (8 * 7 + 4n * 7) + 1 12 + 9n = (56 + 28n) + 1 Reorder the terms: 12 + 9n = 56 + 1 + 28n Combine like terms: 56 + 1 = 57 12 + 9n = 57 + 28n Solving 12 + 9n = 57 + 28n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-28n' to each side of the equation. 12 + 9n + -28n = 57 + 28n + -28n Combine like terms: 9n + -28n = -19n 12 + -19n = 57 + 28n + -28n Combine like terms: 28n + -28n = 0 12 + -19n = 57 + 0 12 + -19n = 57 Add '-12' to each side of the equation. 12 + -12 + -19n = 57 + -12 Combine like terms: 12 + -12 = 0 0 + -19n = 57 + -12 -19n = 57 + -12 Combine like terms: 57 + -12 = 45 -19n = 45 Divide each side by '-19'. n = -2.368421053 Simplifying n = -2.368421053
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