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