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Simplifying 4(4w + 3) + 2w = 8(w + 8) + -32 Reorder the terms: 4(3 + 4w) + 2w = 8(w + 8) + -32 (3 * 4 + 4w * 4) + 2w = 8(w + 8) + -32 (12 + 16w) + 2w = 8(w + 8) + -32 Combine like terms: 16w + 2w = 18w 12 + 18w = 8(w + 8) + -32 Reorder the terms: 12 + 18w = 8(8 + w) + -32 12 + 18w = (8 * 8 + w * 8) + -32 12 + 18w = (64 + 8w) + -32 Reorder the terms: 12 + 18w = 64 + -32 + 8w Combine like terms: 64 + -32 = 32 12 + 18w = 32 + 8w Solving 12 + 18w = 32 + 8w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8w' to each side of the equation. 12 + 18w + -8w = 32 + 8w + -8w Combine like terms: 18w + -8w = 10w 12 + 10w = 32 + 8w + -8w Combine like terms: 8w + -8w = 0 12 + 10w = 32 + 0 12 + 10w = 32 Add '-12' to each side of the equation. 12 + -12 + 10w = 32 + -12 Combine like terms: 12 + -12 = 0 0 + 10w = 32 + -12 10w = 32 + -12 Combine like terms: 32 + -12 = 20 10w = 20 Divide each side by '10'. w = 2 Simplifying w = 2
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