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Simplifying 5x + 4y + 3z + -3x + 2z + -5y = 0 Reorder the terms: 5x + -3x + 4y + -5y + 3z + 2z = 0 Combine like terms: 5x + -3x = 2x 2x + 4y + -5y + 3z + 2z = 0 Combine like terms: 4y + -5y = -1y 2x + -1y + 3z + 2z = 0 Combine like terms: 3z + 2z = 5z 2x + -1y + 5z = 0 Solving 2x + -1y + 5z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 2x + -1y + y + 5z = 0 + y Combine like terms: -1y + y = 0 2x + 0 + 5z = 0 + y 2x + 5z = 0 + y Remove the zero: 2x + 5z = y Add '-5z' to each side of the equation. 2x + 5z + -5z = y + -5z Combine like terms: 5z + -5z = 0 2x + 0 = y + -5z 2x = y + -5z Divide each side by '2'. x = 0.5y + -2.5z Simplifying x = 0.5y + -2.5z
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