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\frac{2}{9}x+4=2
Swap sides so that all variable terms are on the left hand side.
\frac{2}{9}x=2-4
Subtract 4 from both sides.
\frac{2}{9}x=-2
Subtract 4 from 2 to get -2.
x=-2\times \frac{9}{2}
Multiply both sides by \frac{9}{2}, the reciprocal of \frac{2}{9}.
x=-9
Multiply -2 times \frac{9}{2}.