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\frac{2}{3}x+8=10
Swap sides so that all variable terms are on the left hand side.
\frac{2}{3}x=10-8
Subtract 8 from both sides.
\frac{2}{3}x=2
Subtract 8 from 10 to get 2.
x=2\times \frac{3}{2}
Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}.
x=3
Cancel out 2 and 2.