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Simplifying (-6x + -1z) + -1(3y + (7x + -1(3z + 8y + x))) = 0 Remove parenthesis around (-6x + -1z) -6x + -1z + -1(3y + (7x + -1(3z + 8y + x))) = 0 Reorder the terms: -6x + -1z + -1(3y + (7x + -1(x + 8y + 3z))) = 0 -6x + -1z + -1(3y + (7x + (x * -1 + 8y * -1 + 3z * -1))) = 0 -6x + -1z + -1(3y + (7x + (-1x + -8y + -3z))) = 0 Combine like terms: 7x + -1x = 6x -6x + -1z + -1(3y + (6x + -8y + -3z)) = 0 Remove parenthesis around (6x + -8y + -3z) -6x + -1z + -1(3y + 6x + -8y + -3z) = 0 Reorder the terms: -6x + -1z + -1(6x + 3y + -8y + -3z) = 0 Combine like terms: 3y + -8y = -5y -6x + -1z + -1(6x + -5y + -3z) = 0 -6x + -1z + (6x * -1 + -5y * -1 + -3z * -1) = 0 -6x + -1z + (-6x + 5y + 3z) = 0 Reorder the terms: -6x + -6x + 5y + -1z + 3z = 0 Combine like terms: -6x + -6x = -12x -12x + 5y + -1z + 3z = 0 Combine like terms: -1z + 3z = 2z -12x + 5y + 2z = 0 Solving -12x + 5y + 2z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. -12x + 5y + -5y + 2z = 0 + -5y Combine like terms: 5y + -5y = 0 -12x + 0 + 2z = 0 + -5y -12x + 2z = 0 + -5y Remove the zero: -12x + 2z = -5y Add '-2z' to each side of the equation. -12x + 2z + -2z = -5y + -2z Combine like terms: 2z + -2z = 0 -12x + 0 = -5y + -2z -12x = -5y + -2z Divide each side by '-12'. x = 0.4166666667y + 0.1666666667z Simplifying x = 0.4166666667y + 0.1666666667z
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