Lời giải:
BPT \(\Leftrightarrow \left[\begin{matrix} \frac{x-7}{2x+1}>2\\ \frac{x-7}{2x+1}< -2\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} \frac{-3x-9}{2x+1}>0\\ \frac{5x-5}{2x+1}< 0\end{matrix}\right.\)
\(\Leftrightarrow \left[\begin{matrix} \frac{x+3}{2x+1}< 0\\ \frac{x-1}{2x+1}< 0\end{matrix}\right.\)
Với $\frac{x+3}{2x+1}<0$ thì: \(\Leftrightarrow \left[\begin{matrix} x+3< 0; 2x+1>0\\ x+3>0; 2x+1< 0\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} \frac{-1}{2}< x< -3(\text{vô lý})\\ -3< x< \frac{-1}{2}\end{matrix}\right.\)
Với $\frac{x-1}{2x+1}< 0$ thì:
\(\Leftrightarrow \left[\begin{matrix} x-1>0; 2x+1< 0\\ x-1<0; 2x+1>0\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} -\frac{1}{2}>x>1(\text{vô lý})\\ -\frac{1}{2}< x< 1\end{matrix}\right.\)
Vậy $-3< x< \frac{-1}{2}$ hoặc $\frac{-1}{2}< x< 1$