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Simplifying 2(4x + 2y + -1z) = 0 (4x * 2 + 2y * 2 + -1z * 2) = 0 (8x + 4y + -2z) = 0 Solving 8x + 4y + -2z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 8x + 4y + -4y + -2z = 0 + -4y Combine like terms: 4y + -4y = 0 8x + 0 + -2z = 0 + -4y 8x + -2z = 0 + -4y Remove the zero: 8x + -2z = -4y Add '2z' to each side of the equation. 8x + -2z + 2z = -4y + 2z Combine like terms: -2z + 2z = 0 8x + 0 = -4y + 2z 8x = -4y + 2z Divide each side by '8'. x = -0.5y + 0.25z Simplifying x = -0.5y + 0.25z
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