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Simplifying (3x + y + -1z) + -1(3x + -2z) + -1(2x + -6y) = 0 Remove parenthesis around (3x + y + -1z) 3x + y + -1z + -1(3x + -2z) + -1(2x + -6y) = 0 3x + y + -1z + (3x * -1 + -2z * -1) + -1(2x + -6y) = 0 3x + y + -1z + (-3x + 2z) + -1(2x + -6y) = 0 3x + y + -1z + -3x + 2z + (2x * -1 + -6y * -1) = 0 3x + y + -1z + -3x + 2z + (-2x + 6y) = 0 Reorder the terms: 3x + -3x + -2x + y + 6y + -1z + 2z = 0 Combine like terms: 3x + -3x = 0 0 + -2x + y + 6y + -1z + 2z = 0 -2x + y + 6y + -1z + 2z = 0 Combine like terms: y + 6y = 7y -2x + 7y + -1z + 2z = 0 Combine like terms: -1z + 2z = 1z -2x + 7y + 1z = 0 Solving -2x + 7y + 1z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7y' to each side of the equation. -2x + 7y + -7y + 1z = 0 + -7y Combine like terms: 7y + -7y = 0 -2x + 0 + 1z = 0 + -7y -2x + 1z = 0 + -7y Remove the zero: -2x + 1z = -7y Add '-1z' to each side of the equation. -2x + 1z + -1z = -7y + -1z Combine like terms: 1z + -1z = 0 -2x + 0 = -7y + -1z -2x = -7y + -1z Divide each side by '-2'. x = 3.5y + 0.5z Simplifying x = 3.5y + 0.5z
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