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Simplifying 3(2n + 4) + 5(3 + -2n) = 7 + -2n Reorder the terms: 3(4 + 2n) + 5(3 + -2n) = 7 + -2n (4 * 3 + 2n * 3) + 5(3 + -2n) = 7 + -2n (12 + 6n) + 5(3 + -2n) = 7 + -2n 12 + 6n + (3 * 5 + -2n * 5) = 7 + -2n 12 + 6n + (15 + -10n) = 7 + -2n Reorder the terms: 12 + 15 + 6n + -10n = 7 + -2n Combine like terms: 12 + 15 = 27 27 + 6n + -10n = 7 + -2n Combine like terms: 6n + -10n = -4n 27 + -4n = 7 + -2n Solving 27 + -4n = 7 + -2n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2n' to each side of the equation. 27 + -4n + 2n = 7 + -2n + 2n Combine like terms: -4n + 2n = -2n 27 + -2n = 7 + -2n + 2n Combine like terms: -2n + 2n = 0 27 + -2n = 7 + 0 27 + -2n = 7 Add '-27' to each side of the equation. 27 + -27 + -2n = 7 + -27 Combine like terms: 27 + -27 = 0 0 + -2n = 7 + -27 -2n = 7 + -27 Combine like terms: 7 + -27 = -20 -2n = -20 Divide each side by '-2'. n = 10 Simplifying n = 10
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