\[\begin{array}{l}
1 \le \frac{{13 - 2z}}{z} \le \frac{3}{2} \Leftrightarrow \left\{ \begin{array}{l}
\frac{{13 - 2z}}{z} - 1 \ge 0\\
\frac{{13 - 2z}}{z} - \frac{3}{2} \le 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\frac{{13 - 2z - z}}{z} \ge 0\\
\frac{{26 - 4z - 3z}}{{2z}} \le 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
\frac{{13 - 3z}}{z} \ge 0\\
\frac{{26 - 7z}}{{2z}} \le 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
\left\{ \begin{array}{l}
13 - 3z \ge 0\\
z > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
13 - 3z \le 0\\
z < 0
\end{array} \right.
\end{array} \right.\\
\left[ \begin{array}{l}
\left\{ \begin{array}{l}
26 - 7z \ge 0\\
2z < 0
\end{array} \right.\\
\left\{ \begin{array}{l}
26 - 7z \le 0\\
2z > 0
\end{array} \right.
\end{array} \right.
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
\left\{ \begin{array}{l}
z \le \frac{{13}}{2}\\
z > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
z \ge \frac{{13}}{3}\\
z < 0
\end{array} \right.
\end{array} \right.\\
\left[ \begin{array}{l}
\left\{ \begin{array}{l}
z \le \frac{{26}}{7}\\
z < 0
\end{array} \right.\\
\left\{ \begin{array}{l}
z \ge \frac{{26}}{7}\\
z > 0
\end{array} \right.
\end{array} \right.
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
0 < z \le \frac{{13}}{3}\\
\left[ \begin{array}{l}
z < 0\\
z > \frac{{26}}{7}
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \frac{{26}}{7} < z \le \frac{{13}}{3} \Leftrightarrow 3,71 < z \le 4,3.
\end{array}\]