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Simplifying 3w + -2(0.5w + 1) = -4(2 + w) Reorder the terms: 3w + -2(1 + 0.5w) = -4(2 + w) 3w + (1 * -2 + 0.5w * -2) = -4(2 + w) 3w + (-2 + -1w) = -4(2 + w) Reorder the terms: -2 + 3w + -1w = -4(2 + w) Combine like terms: 3w + -1w = 2w -2 + 2w = -4(2 + w) -2 + 2w = (2 * -4 + w * -4) -2 + 2w = (-8 + -4w) Solving -2 + 2w = -8 + -4w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4w' to each side of the equation. -2 + 2w + 4w = -8 + -4w + 4w Combine like terms: 2w + 4w = 6w -2 + 6w = -8 + -4w + 4w Combine like terms: -4w + 4w = 0 -2 + 6w = -8 + 0 -2 + 6w = -8 Add '2' to each side of the equation. -2 + 2 + 6w = -8 + 2 Combine like terms: -2 + 2 = 0 0 + 6w = -8 + 2 6w = -8 + 2 Combine like terms: -8 + 2 = -6 6w = -6 Divide each side by '6'. w = -1 Simplifying w = -1
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