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-\frac{9}{14}x+18+\frac{2}{3}x=17
Add \frac{2}{3}x to both sides.
\frac{1}{42}x+18=17
Combine -\frac{9}{14}x and \frac{2}{3}x to get \frac{1}{42}x.
\frac{1}{42}x=17-18
Subtract 18 from both sides.
\frac{1}{42}x=-1
Subtract 18 from 17 to get -1.
x=-42
Multiply both sides by 42, the reciprocal of \frac{1}{42}.