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Simplifying 2(w + 3) + -5(2 + -1w) + 3(4 + -1w) = 0 Reorder the terms: 2(3 + w) + -5(2 + -1w) + 3(4 + -1w) = 0 (3 * 2 + w * 2) + -5(2 + -1w) + 3(4 + -1w) = 0 (6 + 2w) + -5(2 + -1w) + 3(4 + -1w) = 0 6 + 2w + (2 * -5 + -1w * -5) + 3(4 + -1w) = 0 6 + 2w + (-10 + 5w) + 3(4 + -1w) = 0 6 + 2w + -10 + 5w + (4 * 3 + -1w * 3) = 0 6 + 2w + -10 + 5w + (12 + -3w) = 0 Reorder the terms: 6 + -10 + 12 + 2w + 5w + -3w = 0 Combine like terms: 6 + -10 = -4 -4 + 12 + 2w + 5w + -3w = 0 Combine like terms: -4 + 12 = 8 8 + 2w + 5w + -3w = 0 Combine like terms: 2w + 5w = 7w 8 + 7w + -3w = 0 Combine like terms: 7w + -3w = 4w 8 + 4w = 0 Solving 8 + 4w = 0 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 4w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 4w = 0 + -8 4w = 0 + -8 Combine like terms: 0 + -8 = -8 4w = -8 Divide each side by '4'. w = -2 Simplifying w = -2
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