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Simplifying 2w + 8 + -7w + 1 = 3w + -1 + 2w + -5 Reorder the terms: 8 + 1 + 2w + -7w = 3w + -1 + 2w + -5 Combine like terms: 8 + 1 = 9 9 + 2w + -7w = 3w + -1 + 2w + -5 Combine like terms: 2w + -7w = -5w 9 + -5w = 3w + -1 + 2w + -5 Reorder the terms: 9 + -5w = -1 + -5 + 3w + 2w Combine like terms: -1 + -5 = -6 9 + -5w = -6 + 3w + 2w Combine like terms: 3w + 2w = 5w 9 + -5w = -6 + 5w Solving 9 + -5w = -6 + 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. 9 + -5w + -5w = -6 + 5w + -5w Combine like terms: -5w + -5w = -10w 9 + -10w = -6 + 5w + -5w Combine like terms: 5w + -5w = 0 9 + -10w = -6 + 0 9 + -10w = -6 Add '-9' to each side of the equation. 9 + -9 + -10w = -6 + -9 Combine like terms: 9 + -9 = 0 0 + -10w = -6 + -9 -10w = -6 + -9 Combine like terms: -6 + -9 = -15 -10w = -15 Divide each side by '-10'. w = 1.5 Simplifying w = 1.5
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