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Simplifying 8(2n + 1) = 8(4n + 1) + 5 Reorder the terms: 8(1 + 2n) = 8(4n + 1) + 5 (1 * 8 + 2n * 8) = 8(4n + 1) + 5 (8 + 16n) = 8(4n + 1) + 5 Reorder the terms: 8 + 16n = 8(1 + 4n) + 5 8 + 16n = (1 * 8 + 4n * 8) + 5 8 + 16n = (8 + 32n) + 5 Reorder the terms: 8 + 16n = 8 + 5 + 32n Combine like terms: 8 + 5 = 13 8 + 16n = 13 + 32n Solving 8 + 16n = 13 + 32n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-32n' to each side of the equation. 8 + 16n + -32n = 13 + 32n + -32n Combine like terms: 16n + -32n = -16n 8 + -16n = 13 + 32n + -32n Combine like terms: 32n + -32n = 0 8 + -16n = 13 + 0 8 + -16n = 13 Add '-8' to each side of the equation. 8 + -8 + -16n = 13 + -8 Combine like terms: 8 + -8 = 0 0 + -16n = 13 + -8 -16n = 13 + -8 Combine like terms: 13 + -8 = 5 -16n = 5 Divide each side by '-16'. n = -0.3125 Simplifying n = -0.3125
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