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Simplifying 2v + -1w + 3x + y + -4z = 0 Solving 2v + -1w + 3x + y + -4z = 0 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add 'w' to each side of the equation. 2v + -1w + 3x + y + w + -4z = 0 + w Reorder the terms: 2v + -1w + w + 3x + y + -4z = 0 + w Combine like terms: -1w + w = 0 2v + 0 + 3x + y + -4z = 0 + w 2v + 3x + y + -4z = 0 + w Remove the zero: 2v + 3x + y + -4z = w Add '-3x' to each side of the equation. 2v + 3x + y + -3x + -4z = w + -3x Reorder the terms: 2v + 3x + -3x + y + -4z = w + -3x Combine like terms: 3x + -3x = 0 2v + 0 + y + -4z = w + -3x 2v + y + -4z = w + -3x Add '-1y' to each side of the equation. 2v + y + -1y + -4z = w + -3x + -1y Combine like terms: y + -1y = 0 2v + 0 + -4z = w + -3x + -1y 2v + -4z = w + -3x + -1y Add '4z' to each side of the equation. 2v + -4z + 4z = w + -3x + -1y + 4z Combine like terms: -4z + 4z = 0 2v + 0 = w + -3x + -1y + 4z 2v = w + -3x + -1y + 4z Divide each side by '2'. v = 0.5w + -1.5x + -0.5y + 2z Simplifying v = 0.5w + -1.5x + -0.5y + 2z
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