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Simplifying 5(2n + 1) = 8(3n + 6) + 6 Reorder the terms: 5(1 + 2n) = 8(3n + 6) + 6 (1 * 5 + 2n * 5) = 8(3n + 6) + 6 (5 + 10n) = 8(3n + 6) + 6 Reorder the terms: 5 + 10n = 8(6 + 3n) + 6 5 + 10n = (6 * 8 + 3n * 8) + 6 5 + 10n = (48 + 24n) + 6 Reorder the terms: 5 + 10n = 48 + 6 + 24n Combine like terms: 48 + 6 = 54 5 + 10n = 54 + 24n Solving 5 + 10n = 54 + 24n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-24n' to each side of the equation. 5 + 10n + -24n = 54 + 24n + -24n Combine like terms: 10n + -24n = -14n 5 + -14n = 54 + 24n + -24n Combine like terms: 24n + -24n = 0 5 + -14n = 54 + 0 5 + -14n = 54 Add '-5' to each side of the equation. 5 + -5 + -14n = 54 + -5 Combine like terms: 5 + -5 = 0 0 + -14n = 54 + -5 -14n = 54 + -5 Combine like terms: 54 + -5 = 49 -14n = 49 Divide each side by '-14'. n = -3.5 Simplifying n = -3.5
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