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Simplifying 33 + -2(2w + 1) = 7w + -2(7 + w) Reorder the terms: 33 + -2(1 + 2w) = 7w + -2(7 + w) 33 + (1 * -2 + 2w * -2) = 7w + -2(7 + w) 33 + (-2 + -4w) = 7w + -2(7 + w) Combine like terms: 33 + -2 = 31 31 + -4w = 7w + -2(7 + w) 31 + -4w = 7w + (7 * -2 + w * -2) 31 + -4w = 7w + (-14 + -2w) Reorder the terms: 31 + -4w = -14 + 7w + -2w Combine like terms: 7w + -2w = 5w 31 + -4w = -14 + 5w Solving 31 + -4w = -14 + 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 + -4w + -5w = -14 + 5w + -5w Combine like terms: -4w + -5w = -9w 31 + -9w = -14 + 5w + -5w Combine like terms: 5w + -5w = 0 31 + -9w = -14 + 0 31 + -9w = -14 Add '-31' to each side of the equation. 31 + -31 + -9w = -14 + -31 Combine like terms: 31 + -31 = 0 0 + -9w = -14 + -31 -9w = -14 + -31 Combine like terms: -14 + -31 = -45 -9w = -45 Divide each side by '-9'. w = 5 Simplifying w = 5
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