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Simplifying 31 = 3(w + 7) + -8w Reorder the terms: 31 = 3(7 + w) + -8w 31 = (7 * 3 + w * 3) + -8w 31 = (21 + 3w) + -8w Combine like terms: 3w + -8w = -5w 31 = 21 + -5w Solving 31 = 21 + -5w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '5w' to each side of the equation. 31 + 5w = 21 + -5w + 5w Combine like terms: -5w + 5w = 0 31 + 5w = 21 + 0 31 + 5w = 21 Add '-31' to each side of the equation. 31 + -31 + 5w = 21 + -31 Combine like terms: 31 + -31 = 0 0 + 5w = 21 + -31 5w = 21 + -31 Combine like terms: 21 + -31 = -10 5w = -10 Divide each side by '5'. w = -2 Simplifying w = -2
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