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Simplifying 2(4z + -2x + y) + -4(5z + x + -1y) = 0 Reorder the terms: 2(-2x + y + 4z) + -4(5z + x + -1y) = 0 (-2x * 2 + y * 2 + 4z * 2) + -4(5z + x + -1y) = 0 (-4x + 2y + 8z) + -4(5z + x + -1y) = 0 Reorder the terms: -4x + 2y + 8z + -4(x + -1y + 5z) = 0 -4x + 2y + 8z + (x * -4 + -1y * -4 + 5z * -4) = 0 -4x + 2y + 8z + (-4x + 4y + -20z) = 0 Reorder the terms: -4x + -4x + 2y + 4y + 8z + -20z = 0 Combine like terms: -4x + -4x = -8x -8x + 2y + 4y + 8z + -20z = 0 Combine like terms: 2y + 4y = 6y -8x + 6y + 8z + -20z = 0 Combine like terms: 8z + -20z = -12z -8x + 6y + -12z = 0 Solving -8x + 6y + -12z = 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. -8x + 6y + -6y + -12z = 0 + -6y Combine like terms: 6y + -6y = 0 -8x + 0 + -12z = 0 + -6y -8x + -12z = 0 + -6y Remove the zero: -8x + -12z = -6y Add '12z' to each side of the equation. -8x + -12z + 12z = -6y + 12z Combine like terms: -12z + 12z = 0 -8x + 0 = -6y + 12z -8x = -6y + 12z Divide each side by '-8'. x = 0.75y + -1.5z Simplifying x = 0.75y + -1.5z
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