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Simplifying 8(4 + -1w) = 7(2w + 3) (4 * 8 + -1w * 8) = 7(2w + 3) (32 + -8w) = 7(2w + 3) Reorder the terms: 32 + -8w = 7(3 + 2w) 32 + -8w = (3 * 7 + 2w * 7) 32 + -8w = (21 + 14w) Solving 32 + -8w = 21 + 14w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-14w' to each side of the equation. 32 + -8w + -14w = 21 + 14w + -14w Combine like terms: -8w + -14w = -22w 32 + -22w = 21 + 14w + -14w Combine like terms: 14w + -14w = 0 32 + -22w = 21 + 0 32 + -22w = 21 Add '-32' to each side of the equation. 32 + -32 + -22w = 21 + -32 Combine like terms: 32 + -32 = 0 0 + -22w = 21 + -32 -22w = 21 + -32 Combine like terms: 21 + -32 = -11 -22w = -11 Divide each side by '-22'. w = 0.5 Simplifying w = 0.5
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