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Simplifying 0.5w + 5 = 1w + 2 Reorder the terms: 5 + 0.5w = 1w + 2 Reorder the terms: 5 + 0.5w = 2 + 1w Solving 5 + 0.5w = 2 + 1w 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. 5 + 0.5w + -1w = 2 + 1w + -1w Combine like terms: 0.5w + -1w = -0.5w 5 + -0.5w = 2 + 1w + -1w Combine like terms: 1w + -1w = 0 5 + -0.5w = 2 + 0 5 + -0.5w = 2 Add '-5' to each side of the equation. 5 + -5 + -0.5w = 2 + -5 Combine like terms: 5 + -5 = 0 0 + -0.5w = 2 + -5 -0.5w = 2 + -5 Combine like terms: 2 + -5 = -3 -0.5w = -3 Divide each side by '-0.5'. w = 6 Simplifying w = 6
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