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Simplifying 3v + -2w + 4x + 4y + 12z = 14 Solving 3v + -2w + 4x + 4y + 12z = 14 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '2w' to each side of the equation. 3v + -2w + 4x + 4y + 2w + 12z = 14 + 2w Reorder the terms: 3v + -2w + 2w + 4x + 4y + 12z = 14 + 2w Combine like terms: -2w + 2w = 0 3v + 0 + 4x + 4y + 12z = 14 + 2w 3v + 4x + 4y + 12z = 14 + 2w Add '-4x' to each side of the equation. 3v + 4x + 4y + -4x + 12z = 14 + 2w + -4x Reorder the terms: 3v + 4x + -4x + 4y + 12z = 14 + 2w + -4x Combine like terms: 4x + -4x = 0 3v + 0 + 4y + 12z = 14 + 2w + -4x 3v + 4y + 12z = 14 + 2w + -4x Add '-4y' to each side of the equation. 3v + 4y + -4y + 12z = 14 + 2w + -4x + -4y Combine like terms: 4y + -4y = 0 3v + 0 + 12z = 14 + 2w + -4x + -4y 3v + 12z = 14 + 2w + -4x + -4y Add '-12z' to each side of the equation. 3v + 12z + -12z = 14 + 2w + -4x + -4y + -12z Combine like terms: 12z + -12z = 0 3v + 0 = 14 + 2w + -4x + -4y + -12z 3v = 14 + 2w + -4x + -4y + -12z Divide each side by '3'. v = 4.666666667 + 0.6666666667w + -1.333333333x + -1.333333333y + -4z Simplifying v = 4.666666667 + 0.6666666667w + -1.333333333x + -1.333333333y + -4z
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