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Simplifying 2(3x + 2y + -1z) + 3x = 0 (3x * 2 + 2y * 2 + -1z * 2) + 3x = 0 (6x + 4y + -2z) + 3x = 0 Reorder the terms: 6x + 3x + 4y + -2z = 0 Combine like terms: 6x + 3x = 9x 9x + 4y + -2z = 0 Solving 9x + 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. 9x + 4y + -4y + -2z = 0 + -4y Combine like terms: 4y + -4y = 0 9x + 0 + -2z = 0 + -4y 9x + -2z = 0 + -4y Remove the zero: 9x + -2z = -4y Add '2z' to each side of the equation. 9x + -2z + 2z = -4y + 2z Combine like terms: -2z + 2z = 0 9x + 0 = -4y + 2z 9x = -4y + 2z Divide each side by '9'. x = -0.4444444444y + 0.2222222222z Simplifying x = -0.4444444444y + 0.2222222222z
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