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-\frac{1}{2}x+2-\frac{2}{3}x=9
Subtract \frac{2}{3}x from both sides.
-\frac{7}{6}x+2=9
Combine -\frac{1}{2}x and -\frac{2}{3}x to get -\frac{7}{6}x.
-\frac{7}{6}x=9-2
Subtract 2 from both sides.
-\frac{7}{6}x=7
Subtract 2 from 9 to get 7.
x=7\left(-\frac{6}{7}\right)
Multiply both sides by -\frac{6}{7}, the reciprocal of -\frac{7}{6}.
x=-6
Cancel out 7 and 7.