Bài 1:
Ta có: \(\frac{x-1}{2}-2x+1>\frac{x-2}{2}\)
\(\Leftrightarrow\frac{x-1}{2}-2x+1-\frac{x-2}{2}>0\)
\(\Leftrightarrow\frac{x-1}{2}-\frac{4x}{2}+\frac{2}{2}-\frac{x-2}{2}>0\)
\(\Leftrightarrow x-1-4x+2-x+2>0\)
\(\Leftrightarrow-4x+3>0\)
\(\Leftrightarrow-4x>-3\)
\(\Leftrightarrow x< \frac{3}{4}\)
Vậy: Tập nghiệm \(x< \frac{3}{4}\)
Bài 2:
Ta có: |2x-1|=5x-4
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=5x-4\\2x-1=4-5x\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x-1-5x+4=0\\2x-1-4+5x=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}-3x+3=0\\7x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-3x=-3\\7x=5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\frac{5}{7}\end{matrix}\right.\)
Vậy: Tập nghiệm \(S=\left\{1;\frac{5}{7}\right\}\)