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Simplifying (2x + 7y + -4z) + -1(3x + 3y + -6z) = 0 Remove parenthesis around (2x + 7y + -4z) 2x + 7y + -4z + -1(3x + 3y + -6z) = 0 2x + 7y + -4z + (3x * -1 + 3y * -1 + -6z * -1) = 0 2x + 7y + -4z + (-3x + -3y + 6z) = 0 Reorder the terms: 2x + -3x + 7y + -3y + -4z + 6z = 0 Combine like terms: 2x + -3x = -1x -1x + 7y + -3y + -4z + 6z = 0 Combine like terms: 7y + -3y = 4y -1x + 4y + -4z + 6z = 0 Combine like terms: -4z + 6z = 2z -1x + 4y + 2z = 0 Solving -1x + 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. -1x + 4y + -4y + 2z = 0 + -4y Combine like terms: 4y + -4y = 0 -1x + 0 + 2z = 0 + -4y -1x + 2z = 0 + -4y Remove the zero: -1x + 2z = -4y Add '-2z' to each side of the equation. -1x + 2z + -2z = -4y + -2z Combine like terms: 2z + -2z = 0 -1x + 0 = -4y + -2z -1x = -4y + -2z Divide each side by '-1'. x = 4y + 2z Simplifying x = 4y + 2z
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