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Simplifying -2(-4v + w) + 6(-3w + 5v) = 0 (-4v * -2 + w * -2) + 6(-3w + 5v) = 0 (8v + -2w) + 6(-3w + 5v) = 0 Reorder the terms: 8v + -2w + 6(5v + -3w) = 0 8v + -2w + (5v * 6 + -3w * 6) = 0 8v + -2w + (30v + -18w) = 0 Reorder the terms: 8v + 30v + -2w + -18w = 0 Combine like terms: 8v + 30v = 38v 38v + -2w + -18w = 0 Combine like terms: -2w + -18w = -20w 38v + -20w = 0 Solving 38v + -20w = 0 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '20w' to each side of the equation. 38v + -20w + 20w = 0 + 20w Combine like terms: -20w + 20w = 0 38v + 0 = 0 + 20w 38v = 0 + 20w Remove the zero: 38v = 20w Divide each side by '38'. v = 0.5263157895w Simplifying v = 0.5263157895w
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