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