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Simplifying 5(2n + 1) = 6(7n + 8) + 6 Reorder the terms: 5(1 + 2n) = 6(7n + 8) + 6 (1 * 5 + 2n * 5) = 6(7n + 8) + 6 (5 + 10n) = 6(7n + 8) + 6 Reorder the terms: 5 + 10n = 6(8 + 7n) + 6 5 + 10n = (8 * 6 + 7n * 6) + 6 5 + 10n = (48 + 42n) + 6 Reorder the terms: 5 + 10n = 48 + 6 + 42n Combine like terms: 48 + 6 = 54 5 + 10n = 54 + 42n Solving 5 + 10n = 54 + 42n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-42n' to each side of the equation. 5 + 10n + -42n = 54 + 42n + -42n Combine like terms: 10n + -42n = -32n 5 + -32n = 54 + 42n + -42n Combine like terms: 42n + -42n = 0 5 + -32n = 54 + 0 5 + -32n = 54 Add '-5' to each side of the equation. 5 + -5 + -32n = 54 + -5 Combine like terms: 5 + -5 = 0 0 + -32n = 54 + -5 -32n = 54 + -5 Combine like terms: 54 + -5 = 49 -32n = 49 Divide each side by '-32'. n = -1.53125 Simplifying n = -1.53125
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