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Simplifying 0.5(4x + 2y + -1z) = 0 (4x * 0.5 + 2y * 0.5 + -1z * 0.5) = 0 (2x + 1y + -0.5z) = 0 Solving 2x + 1y + -0.5z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 2x + 1y + -1y + -0.5z = 0 + -1y Combine like terms: 1y + -1y = 0 2x + 0 + -0.5z = 0 + -1y 2x + -0.5z = 0 + -1y Remove the zero: 2x + -0.5z = -1y Add '0.5z' to each side of the equation. 2x + -0.5z + 0.5z = -1y + 0.5z Combine like terms: -0.5z + 0.5z = 0.0 2x + 0.0 = -1y + 0.5z 2x = -1y + 0.5z Divide each side by '2'. x = -0.5y + 0.25z Simplifying x = -0.5y + 0.25z
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