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Simplifying 0.5(3 + -1w) = w + 9 (3 * 0.5 + -1w * 0.5) = w + 9 (1.5 + -0.5w) = w + 9 Reorder the terms: 1.5 + -0.5w = 9 + w Solving 1.5 + -0.5w = 9 + w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1w' to each side of the equation. 1.5 + -0.5w + -1w = 9 + w + -1w Combine like terms: -0.5w + -1w = -1.5w 1.5 + -1.5w = 9 + w + -1w Combine like terms: w + -1w = 0 1.5 + -1.5w = 9 + 0 1.5 + -1.5w = 9 Add '-1.5' to each side of the equation. 1.5 + -1.5 + -1.5w = 9 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -1.5w = 9 + -1.5 -1.5w = 9 + -1.5 Combine like terms: 9 + -1.5 = 7.5 -1.5w = 7.5 Divide each side by '-1.5'. w = -5 Simplifying w = -5
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