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Simplifying 5(3n + 1) = 8(6n + 9) + 1 Reorder the terms: 5(1 + 3n) = 8(6n + 9) + 1 (1 * 5 + 3n * 5) = 8(6n + 9) + 1 (5 + 15n) = 8(6n + 9) + 1 Reorder the terms: 5 + 15n = 8(9 + 6n) + 1 5 + 15n = (9 * 8 + 6n * 8) + 1 5 + 15n = (72 + 48n) + 1 Reorder the terms: 5 + 15n = 72 + 1 + 48n Combine like terms: 72 + 1 = 73 5 + 15n = 73 + 48n Solving 5 + 15n = 73 + 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. 5 + 15n + -48n = 73 + 48n + -48n Combine like terms: 15n + -48n = -33n 5 + -33n = 73 + 48n + -48n Combine like terms: 48n + -48n = 0 5 + -33n = 73 + 0 5 + -33n = 73 Add '-5' to each side of the equation. 5 + -5 + -33n = 73 + -5 Combine like terms: 5 + -5 = 0 0 + -33n = 73 + -5 -33n = 73 + -5 Combine like terms: 73 + -5 = 68 -33n = 68 Divide each side by '-33'. n = -2.060606061 Simplifying n = -2.060606061
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