Simplify \(\frac{1}{3}(2x+1)\) to \(\frac{2x+1}{3}\).
\[\frac{2x+1}{3}-\frac{1}{2}(x-1)=\frac{5}{6}\]
Simplify \(\frac{1}{2}(x-1)\) to \(\frac{x-1}{2}\).
\[\frac{2x+1}{3}-\frac{x-1}{2}=\frac{5}{6}\]
Multiply both sides by \(6\) (the LCM of \(3, 2\)).
\[2(2x+1)-3(x-1)=5\]
Expand.
\[4x+2-3x+3=5\]
Simplify \(4x+2-3x+3\) to \(x+5\).
\[x+5=5\]
Cancel \(5\) on both sides.
\[x=0\]
x=0
