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