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Simplifying 0.5(12w + 8) + -0.2(10w + -5) = 0 Reorder the terms: 0.5(8 + 12w) + -0.2(10w + -5) = 0 (8 * 0.5 + 12w * 0.5) + -0.2(10w + -5) = 0 (4 + 6w) + -0.2(10w + -5) = 0 Reorder the terms: 4 + 6w + -0.2(-5 + 10w) = 0 4 + 6w + (-5 * -0.2 + 10w * -0.2) = 0 4 + 6w + (1 + -2w) = 0 Reorder the terms: 4 + 1 + 6w + -2w = 0 Combine like terms: 4 + 1 = 5 5 + 6w + -2w = 0 Combine like terms: 6w + -2w = 4w 5 + 4w = 0 Solving 5 + 4w = 0 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4w = 0 + -5 4w = 0 + -5 Combine like terms: 0 + -5 = -5 4w = -5 Divide each side by '4'. w = -1.25 Simplifying w = -1.25
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