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Simplifying (x + y + 4z) + -1(4x + -6y + z) = 0 Remove parenthesis around (x + y + 4z) x + y + 4z + -1(4x + -6y + z) = 0 x + y + 4z + (4x * -1 + -6y * -1 + z * -1) = 0 x + y + 4z + (-4x + 6y + -1z) = 0 Reorder the terms: x + -4x + y + 6y + 4z + -1z = 0 Combine like terms: x + -4x = -3x -3x + y + 6y + 4z + -1z = 0 Combine like terms: y + 6y = 7y -3x + 7y + 4z + -1z = 0 Combine like terms: 4z + -1z = 3z -3x + 7y + 3z = 0 Solving -3x + 7y + 3z = 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. -3x + 7y + -7y + 3z = 0 + -7y Combine like terms: 7y + -7y = 0 -3x + 0 + 3z = 0 + -7y -3x + 3z = 0 + -7y Remove the zero: -3x + 3z = -7y Add '-3z' to each side of the equation. -3x + 3z + -3z = -7y + -3z Combine like terms: 3z + -3z = 0 -3x + 0 = -7y + -3z -3x = -7y + -3z Divide each side by '-3'. x = 2.333333333y + z Simplifying x = 2.333333333y + z
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