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Simplifying 4w + 3w + -6w + -6w = w + 15 + 2w + -31 Combine like terms: 4w + 3w = 7w 7w + -6w + -6w = w + 15 + 2w + -31 Combine like terms: 7w + -6w = 1w 1w + -6w = w + 15 + 2w + -31 Combine like terms: 1w + -6w = -5w -5w = w + 15 + 2w + -31 Reorder the terms: -5w = 15 + -31 + w + 2w Combine like terms: 15 + -31 = -16 -5w = -16 + w + 2w Combine like terms: w + 2w = 3w -5w = -16 + 3w Solving -5w = -16 + 3w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3w' to each side of the equation. -5w + -3w = -16 + 3w + -3w Combine like terms: -5w + -3w = -8w -8w = -16 + 3w + -3w Combine like terms: 3w + -3w = 0 -8w = -16 + 0 -8w = -16 Divide each side by '-8'. w = 2 Simplifying w = 2
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