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Simplifying 5(2n + 3) = 8(4n + 6) + 9 Reorder the terms: 5(3 + 2n) = 8(4n + 6) + 9 (3 * 5 + 2n * 5) = 8(4n + 6) + 9 (15 + 10n) = 8(4n + 6) + 9 Reorder the terms: 15 + 10n = 8(6 + 4n) + 9 15 + 10n = (6 * 8 + 4n * 8) + 9 15 + 10n = (48 + 32n) + 9 Reorder the terms: 15 + 10n = 48 + 9 + 32n Combine like terms: 48 + 9 = 57 15 + 10n = 57 + 32n Solving 15 + 10n = 57 + 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. 15 + 10n + -32n = 57 + 32n + -32n Combine like terms: 10n + -32n = -22n 15 + -22n = 57 + 32n + -32n Combine like terms: 32n + -32n = 0 15 + -22n = 57 + 0 15 + -22n = 57 Add '-15' to each side of the equation. 15 + -15 + -22n = 57 + -15 Combine like terms: 15 + -15 = 0 0 + -22n = 57 + -15 -22n = 57 + -15 Combine like terms: 57 + -15 = 42 -22n = 42 Divide each side by '-22'. n = -1.909090909 Simplifying n = -1.909090909
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