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Simplifying 4(1 + 8n) + 6(8 + -3n) = -1 + 3n + n + 3 (1 * 4 + 8n * 4) + 6(8 + -3n) = -1 + 3n + n + 3 (4 + 32n) + 6(8 + -3n) = -1 + 3n + n + 3 4 + 32n + (8 * 6 + -3n * 6) = -1 + 3n + n + 3 4 + 32n + (48 + -18n) = -1 + 3n + n + 3 Reorder the terms: 4 + 48 + 32n + -18n = -1 + 3n + n + 3 Combine like terms: 4 + 48 = 52 52 + 32n + -18n = -1 + 3n + n + 3 Combine like terms: 32n + -18n = 14n 52 + 14n = -1 + 3n + n + 3 Reorder the terms: 52 + 14n = -1 + 3 + 3n + n Combine like terms: -1 + 3 = 2 52 + 14n = 2 + 3n + n Combine like terms: 3n + n = 4n 52 + 14n = 2 + 4n Solving 52 + 14n = 2 + 4n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4n' to each side of the equation. 52 + 14n + -4n = 2 + 4n + -4n Combine like terms: 14n + -4n = 10n 52 + 10n = 2 + 4n + -4n Combine like terms: 4n + -4n = 0 52 + 10n = 2 + 0 52 + 10n = 2 Add '-52' to each side of the equation. 52 + -52 + 10n = 2 + -52 Combine like terms: 52 + -52 = 0 0 + 10n = 2 + -52 10n = 2 + -52 Combine like terms: 2 + -52 = -50 10n = -50 Divide each side by '10'. n = -5 Simplifying n = -5
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