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Simplifying -6(0.3x + y + 4z) + -1(x + -1y + -1z) = 0 (0.3x * -6 + y * -6 + 4z * -6) + -1(x + -1y + -1z) = 0 (-1.8x + -6y + -24z) + -1(x + -1y + -1z) = 0 -1.8x + -6y + -24z + (x * -1 + -1y * -1 + -1z * -1) = 0 -1.8x + -6y + -24z + (-1x + 1y + 1z) = 0 Reorder the terms: -1.8x + -1x + -6y + 1y + -24z + 1z = 0 Combine like terms: -1.8x + -1x = -2.8x -2.8x + -6y + 1y + -24z + 1z = 0 Combine like terms: -6y + 1y = -5y -2.8x + -5y + -24z + 1z = 0 Combine like terms: -24z + 1z = -23z -2.8x + -5y + -23z = 0 Solving -2.8x + -5y + -23z = 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. -2.8x + -5y + 5y + -23z = 0 + 5y Combine like terms: -5y + 5y = 0 -2.8x + 0 + -23z = 0 + 5y -2.8x + -23z = 0 + 5y Remove the zero: -2.8x + -23z = 5y Add '23z' to each side of the equation. -2.8x + -23z + 23z = 5y + 23z Combine like terms: -23z + 23z = 0 -2.8x + 0 = 5y + 23z -2.8x = 5y + 23z Divide each side by '-2.8'. x = -1.785714286y + -8.214285714z Simplifying x = -1.785714286y + -8.214285714z
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