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Simplifying 5(3n + 1) = 7(4n + 8) + 1 Reorder the terms: 5(1 + 3n) = 7(4n + 8) + 1 (1 * 5 + 3n * 5) = 7(4n + 8) + 1 (5 + 15n) = 7(4n + 8) + 1 Reorder the terms: 5 + 15n = 7(8 + 4n) + 1 5 + 15n = (8 * 7 + 4n * 7) + 1 5 + 15n = (56 + 28n) + 1 Reorder the terms: 5 + 15n = 56 + 1 + 28n Combine like terms: 56 + 1 = 57 5 + 15n = 57 + 28n Solving 5 + 15n = 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. 5 + 15n + -28n = 57 + 28n + -28n Combine like terms: 15n + -28n = -13n 5 + -13n = 57 + 28n + -28n Combine like terms: 28n + -28n = 0 5 + -13n = 57 + 0 5 + -13n = 57 Add '-5' to each side of the equation. 5 + -5 + -13n = 57 + -5 Combine like terms: 5 + -5 = 0 0 + -13n = 57 + -5 -13n = 57 + -5 Combine like terms: 57 + -5 = 52 -13n = 52 Divide each side by '-13'. n = -4 Simplifying n = -4
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