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Simplifying 6n + 31 = 1 + 6(1 + 3n) Reorder the terms: 31 + 6n = 1 + 6(1 + 3n) 31 + 6n = 1 + (1 * 6 + 3n * 6) 31 + 6n = 1 + (6 + 18n) Combine like terms: 1 + 6 = 7 31 + 6n = 7 + 18n Solving 31 + 6n = 7 + 18n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-18n' to each side of the equation. 31 + 6n + -18n = 7 + 18n + -18n Combine like terms: 6n + -18n = -12n 31 + -12n = 7 + 18n + -18n Combine like terms: 18n + -18n = 0 31 + -12n = 7 + 0 31 + -12n = 7 Add '-31' to each side of the equation. 31 + -31 + -12n = 7 + -31 Combine like terms: 31 + -31 = 0 0 + -12n = 7 + -31 -12n = 7 + -31 Combine like terms: 7 + -31 = -24 -12n = -24 Divide each side by '-12'. n = 2 Simplifying n = 2
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