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Simplifying 5(2n + 1) = 8(4n + 2) + 7 Reorder the terms: 5(1 + 2n) = 8(4n + 2) + 7 (1 * 5 + 2n * 5) = 8(4n + 2) + 7 (5 + 10n) = 8(4n + 2) + 7 Reorder the terms: 5 + 10n = 8(2 + 4n) + 7 5 + 10n = (2 * 8 + 4n * 8) + 7 5 + 10n = (16 + 32n) + 7 Reorder the terms: 5 + 10n = 16 + 7 + 32n Combine like terms: 16 + 7 = 23 5 + 10n = 23 + 32n Solving 5 + 10n = 23 + 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. 5 + 10n + -32n = 23 + 32n + -32n Combine like terms: 10n + -32n = -22n 5 + -22n = 23 + 32n + -32n Combine like terms: 32n + -32n = 0 5 + -22n = 23 + 0 5 + -22n = 23 Add '-5' to each side of the equation. 5 + -5 + -22n = 23 + -5 Combine like terms: 5 + -5 = 0 0 + -22n = 23 + -5 -22n = 23 + -5 Combine like terms: 23 + -5 = 18 -22n = 18 Divide each side by '-22'. n = -0.8181818182 Simplifying n = -0.8181818182
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