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Simplifying 14 + -8 + 0.5(4 + w) = 9 + 4(0.8 + 0.8w) 14 + -8 + (4 * 0.5 + w * 0.5) = 9 + 4(0.8 + 0.8w) 14 + -8 + (2 + 0.5w) = 9 + 4(0.8 + 0.8w) Combine like terms: 14 + -8 = 6 6 + 2 + 0.5w = 9 + 4(0.8 + 0.8w) Combine like terms: 6 + 2 = 8 8 + 0.5w = 9 + 4(0.8 + 0.8w) 8 + 0.5w = 9 + (0.8 * 4 + 0.8w * 4) 8 + 0.5w = 9 + (3.2 + 3.2w) Combine like terms: 9 + 3.2 = 12.2 8 + 0.5w = 12.2 + 3.2w Solving 8 + 0.5w = 12.2 + 3.2w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3.2w' to each side of the equation. 8 + 0.5w + -3.2w = 12.2 + 3.2w + -3.2w Combine like terms: 0.5w + -3.2w = -2.7w 8 + -2.7w = 12.2 + 3.2w + -3.2w Combine like terms: 3.2w + -3.2w = 0.0 8 + -2.7w = 12.2 + 0.0 8 + -2.7w = 12.2 Add '-8' to each side of the equation. 8 + -8 + -2.7w = 12.2 + -8 Combine like terms: 8 + -8 = 0 0 + -2.7w = 12.2 + -8 -2.7w = 12.2 + -8 Combine like terms: 12.2 + -8 = 4.2 -2.7w = 4.2 Divide each side by '-2.7'. w = -1.555555556 Simplifying w = -1.555555556
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