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Simplifying 0.5(w + 1) = 2.5w + -7.5 Reorder the terms: 0.5(1 + w) = 2.5w + -7.5 (1 * 0.5 + w * 0.5) = 2.5w + -7.5 (0.5 + 0.5w) = 2.5w + -7.5 Reorder the terms: 0.5 + 0.5w = -7.5 + 2.5w Solving 0.5 + 0.5w = -7.5 + 2.5w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5w' to each side of the equation. 0.5 + 0.5w + -2.5w = -7.5 + 2.5w + -2.5w Combine like terms: 0.5w + -2.5w = -2w 0.5 + -2w = -7.5 + 2.5w + -2.5w Combine like terms: 2.5w + -2.5w = 0.0 0.5 + -2w = -7.5 + 0.0 0.5 + -2w = -7.5 Add '-0.5' to each side of the equation. 0.5 + -0.5 + -2w = -7.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -2w = -7.5 + -0.5 -2w = -7.5 + -0.5 Combine like terms: -7.5 + -0.5 = -8 -2w = -8 Divide each side by '-2'. w = 4 Simplifying w = 4
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