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Simplifying -4x + 5y + -7z + 3x + 5z + -2y = 0 Reorder the terms: -4x + 3x + 5y + -2y + -7z + 5z = 0 Combine like terms: -4x + 3x = -1x -1x + 5y + -2y + -7z + 5z = 0 Combine like terms: 5y + -2y = 3y -1x + 3y + -7z + 5z = 0 Combine like terms: -7z + 5z = -2z -1x + 3y + -2z = 0 Solving -1x + 3y + -2z = 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 + -2z = 0 + -3y Combine like terms: 3y + -3y = 0 -1x + 0 + -2z = 0 + -3y -1x + -2z = 0 + -3y Remove the zero: -1x + -2z = -3y Add '2z' to each side of the equation. -1x + -2z + 2z = -3y + 2z Combine like terms: -2z + 2z = 0 -1x + 0 = -3y + 2z -1x = -3y + 2z Divide each side by '-1'. x = 3y + -2z Simplifying x = 3y + -2z
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