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Simplifying 4(8 + -1w) = 2(3w + 41) (8 * 4 + -1w * 4) = 2(3w + 41) (32 + -4w) = 2(3w + 41) Reorder the terms: 32 + -4w = 2(41 + 3w) 32 + -4w = (41 * 2 + 3w * 2) 32 + -4w = (82 + 6w) Solving 32 + -4w = 82 + 6w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6w' to each side of the equation. 32 + -4w + -6w = 82 + 6w + -6w Combine like terms: -4w + -6w = -10w 32 + -10w = 82 + 6w + -6w Combine like terms: 6w + -6w = 0 32 + -10w = 82 + 0 32 + -10w = 82 Add '-32' to each side of the equation. 32 + -32 + -10w = 82 + -32 Combine like terms: 32 + -32 = 0 0 + -10w = 82 + -32 -10w = 82 + -32 Combine like terms: 82 + -32 = 50 -10w = 50 Divide each side by '-10'. w = -5 Simplifying w = -5
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