Multiply both sides by \(x-2\).
\[x+2=\frac{2}{3}(x-2)\]
Simplify \(\frac{2}{3}(x-2)\) to \(\frac{2(x-2)}{3}\).
\[x+2=\frac{2(x-2)}{3}\]
Multiply both sides by \(3\).
\[3x+6=2(x-2)\]
Expand.
\[3x+6=2x-4\]
Subtract \(2x\) from both sides.
\[3x+6-2x=-4\]
Simplify \(3x+6-2x\) to \(x+6\).
\[x+6=-4\]
Subtract \(6\) from both sides.
\[x=-4-6\]
Simplify \(-4-6\) to \(-10\).
\[x=-10\]
x=-10
