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Simplifying 0.1(w + 0.5) + 0.2w = 0.2(w + -0.4) Reorder the terms: 0.1(0.5 + w) + 0.2w = 0.2(w + -0.4) (0.5 * 0.1 + w * 0.1) + 0.2w = 0.2(w + -0.4) (0.05 + 0.1w) + 0.2w = 0.2(w + -0.4) Combine like terms: 0.1w + 0.2w = 0.3w 0.05 + 0.3w = 0.2(w + -0.4) Reorder the terms: 0.05 + 0.3w = 0.2(-0.4 + w) 0.05 + 0.3w = (-0.4 * 0.2 + w * 0.2) 0.05 + 0.3w = (-0.08 + 0.2w) Solving 0.05 + 0.3w = -0.08 + 0.2w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.2w' to each side of the equation. 0.05 + 0.3w + -0.2w = -0.08 + 0.2w + -0.2w Combine like terms: 0.3w + -0.2w = 0.1w 0.05 + 0.1w = -0.08 + 0.2w + -0.2w Combine like terms: 0.2w + -0.2w = 0.0 0.05 + 0.1w = -0.08 + 0.0 0.05 + 0.1w = -0.08 Add '-0.05' to each side of the equation. 0.05 + -0.05 + 0.1w = -0.08 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + 0.1w = -0.08 + -0.05 0.1w = -0.08 + -0.05 Combine like terms: -0.08 + -0.05 = -0.13 0.1w = -0.13 Divide each side by '0.1'. w = -1.3 Simplifying w = -1.3
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