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Simplifying 3v + -8w + 2x + -1y + 4z = 0 Solving 3v + -8w + 2x + -1y + 4z = 0 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '8w' to each side of the equation. 3v + -8w + 2x + -1y + 8w + 4z = 0 + 8w Reorder the terms: 3v + -8w + 8w + 2x + -1y + 4z = 0 + 8w Combine like terms: -8w + 8w = 0 3v + 0 + 2x + -1y + 4z = 0 + 8w 3v + 2x + -1y + 4z = 0 + 8w Remove the zero: 3v + 2x + -1y + 4z = 8w Add '-2x' to each side of the equation. 3v + 2x + -1y + -2x + 4z = 8w + -2x Reorder the terms: 3v + 2x + -2x + -1y + 4z = 8w + -2x Combine like terms: 2x + -2x = 0 3v + 0 + -1y + 4z = 8w + -2x 3v + -1y + 4z = 8w + -2x Add 'y' to each side of the equation. 3v + -1y + y + 4z = 8w + -2x + y Combine like terms: -1y + y = 0 3v + 0 + 4z = 8w + -2x + y 3v + 4z = 8w + -2x + y Add '-4z' to each side of the equation. 3v + 4z + -4z = 8w + -2x + y + -4z Combine like terms: 4z + -4z = 0 3v + 0 = 8w + -2x + y + -4z 3v = 8w + -2x + y + -4z Divide each side by '3'. v = 2.666666667w + -0.6666666667x + 0.3333333333y + -1.333333333z Simplifying v = 2.666666667w + -0.6666666667x + 0.3333333333y + -1.333333333z
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