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Simplifying 0 = 0.5(12w + 8) + -0.2(10w + -5) Reorder the terms: 0 = 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) Reorder the terms: 0 = 4 + 6w + -0.2(-5 + 10w) 0 = 4 + 6w + (-5 * -0.2 + 10w * -0.2) 0 = 4 + 6w + (1 + -2w) Reorder the terms: 0 = 4 + 1 + 6w + -2w Combine like terms: 4 + 1 = 5 0 = 5 + 6w + -2w Combine like terms: 6w + -2w = 4w 0 = 5 + 4w Solving 0 = 5 + 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. 0 + -4w = 5 + 4w + -4w Remove the zero: -4w = 5 + 4w + -4w Combine like terms: 4w + -4w = 0 -4w = 5 + 0 -4w = 5 Divide each side by '-4'. w = -1.25 Simplifying w = -1.25
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