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Simplifying 9x + 4y + 7z + -4X + 5Z + -6Y = 0 Reorder the terms: -4X + -6Y + 5Z + 9x + 4y + 7z = 0 Solving -4X + -6Y + 5Z + 9x + 4y + 7z = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6Y' to each side of the equation. -4X + -6Y + 5Z + 9x + 4y + 6Y + 7z = 0 + 6Y Reorder the terms: -4X + -6Y + 6Y + 5Z + 9x + 4y + 7z = 0 + 6Y Combine like terms: -6Y + 6Y = 0 -4X + 0 + 5Z + 9x + 4y + 7z = 0 + 6Y -4X + 5Z + 9x + 4y + 7z = 0 + 6Y Remove the zero: -4X + 5Z + 9x + 4y + 7z = 6Y Add '-5Z' to each side of the equation. -4X + 5Z + 9x + 4y + -5Z + 7z = 6Y + -5Z Reorder the terms: -4X + 5Z + -5Z + 9x + 4y + 7z = 6Y + -5Z Combine like terms: 5Z + -5Z = 0 -4X + 0 + 9x + 4y + 7z = 6Y + -5Z -4X + 9x + 4y + 7z = 6Y + -5Z Add '-9x' to each side of the equation. -4X + 9x + 4y + -9x + 7z = 6Y + -5Z + -9x Reorder the terms: -4X + 9x + -9x + 4y + 7z = 6Y + -5Z + -9x Combine like terms: 9x + -9x = 0 -4X + 0 + 4y + 7z = 6Y + -5Z + -9x -4X + 4y + 7z = 6Y + -5Z + -9x Add '-4y' to each side of the equation. -4X + 4y + -4y + 7z = 6Y + -5Z + -9x + -4y Combine like terms: 4y + -4y = 0 -4X + 0 + 7z = 6Y + -5Z + -9x + -4y -4X + 7z = 6Y + -5Z + -9x + -4y Add '-7z' to each side of the equation. -4X + 7z + -7z = 6Y + -5Z + -9x + -4y + -7z Combine like terms: 7z + -7z = 0 -4X + 0 = 6Y + -5Z + -9x + -4y + -7z -4X = 6Y + -5Z + -9x + -4y + -7z Divide each side by '-4'. X = -1.5Y + 1.25Z + 2.25x + y + 1.75z Simplifying X = -1.5Y + 1.25Z + 2.25x + y + 1.75z
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