Factor out the common term \(2\).
\[\frac{2(p-1)}{4}-\frac{3p-1}{2}=\frac{1}{2}-p\]
Simplify \(\frac{2(p-1)}{4}\) to \(\frac{p-1}{2}\).
\[\frac{p-1}{2}-\frac{3p-1}{2}=\frac{1}{2}-p\]
Join the denominators.
\[\frac{p-1-(3p-1)}{2}=\frac{1}{2}-p\]
Remove parentheses.
\[\frac{p-1-3p+1}{2}=\frac{1}{2}-p\]
Simplify \(p-1-3p+1\) to \(-2p\).
\[\frac{-2p}{2}=\frac{1}{2}-p\]
Move the negative sign to the left.
\[-\frac{2p}{2}=\frac{1}{2}-p\]
Cancel \(2\).
\[-p=\frac{1}{2}-p\]
Cancel \(-p\) on both sides.
\[0=\frac{1}{2}\]
Since \(0=\frac{1}{2}\) is false, there is no solution.
[No Solution]
