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Simplifying -2(4v + -1w) + 4(3w + 4v) = 0 (4v * -2 + -1w * -2) + 4(3w + 4v) = 0 (-8v + 2w) + 4(3w + 4v) = 0 Reorder the terms: -8v + 2w + 4(4v + 3w) = 0 -8v + 2w + (4v * 4 + 3w * 4) = 0 -8v + 2w + (16v + 12w) = 0 Reorder the terms: -8v + 16v + 2w + 12w = 0 Combine like terms: -8v + 16v = 8v 8v + 2w + 12w = 0 Combine like terms: 2w + 12w = 14w 8v + 14w = 0 Solving 8v + 14w = 0 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-14w' to each side of the equation. 8v + 14w + -14w = 0 + -14w Combine like terms: 14w + -14w = 0 8v + 0 = 0 + -14w 8v = 0 + -14w Remove the zero: 8v = -14w Divide each side by '8'. v = -1.75w Simplifying v = -1.75w
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