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-\frac{9}{14}x=6
Combine \frac{6}{7}x and -\frac{3}{2}x to get -\frac{9}{14}x.
x=6\left(-\frac{14}{9}\right)
Multiply both sides by -\frac{14}{9}, the reciprocal of -\frac{9}{14}.
x=\frac{6\left(-14\right)}{9}
Express 6\left(-\frac{14}{9}\right) as a single fraction.
x=\frac{-84}{9}
Multiply 6 and -14 to get -84.
x=-\frac{28}{3}
Reduce the fraction \frac{-84}{9} to lowest terms by extracting and canceling out 3.