Solve the system of inequalities for $\mathbf{x}$, and discuss their solutions:
$$
\left\{\begin{array}{l}
\mathrm{m}(\mathbf{x}-1)>\mathbf{x}-2 . \\
3(\mathrm{~m}+1) \mathrm{x}>3 \mathrm{~m} \mathbf{x}+5 .
\end{array} \text { ( } \mathrm{m}\right. \text { is a real parameter) }
$$
$$
\begin{array}{l}
\text { Solve } \begin{array}{l}
m(x-1)>x-2 . \\
3(m+1) x>3 m x+5
\end{array} \\
\Leftrightarrow\left\{\begin{array}{l}
m x-m>x-2 \\
3 m x+3 x>3 m x+5
\end{array}\right. \\
\Leftrightarrow\left\{\begin{array}{r}
(m-1) x>m-2 . \\
x>\frac{5}{3} .
\end{array}\right.
\end{array}
$$
1. If $m=1$.
(I) $\Leftrightarrow\left\{\begin{array}{l}0>-1 \\ x>\frac{5}{3} \Leftrightarrow x>\frac{5}{3} .\end{array}\right.$
2. If $m>1$,
$$
\text { (I) } \Leftrightarrow\left\{\begin{array}{l}
x>\frac{m-2}{m-1}, \\
x>\frac{5}{3} .
\end{array}\right.
$$
(1) Consider $-\frac{m-2}{m-1} \geqslant \frac{5}{3} \Leftrightarrow m \leqslant-\frac{1}{2}$. In this case, (I) has no solution;
(2) Consider $\frac{m-2}{m-1}-\frac{1}{2}$. In this case $m>1$, (I) $\Longleftrightarrow x>\frac{5}{3}$.
3. If $m<1$,
$$
\text { (I) } \Leftrightarrow\left\{\begin{array}{l}
x<\frac{m-2}{m-1}, \\
x>\frac{5}{3} .
\end{array}\right.
$$
(1) Consider $\frac{m-2}{m-1}>\frac{5}{3} \Leftrightarrow m>-\frac{1}{2}$. In this case $-\frac{1}{2}<m<1$, (I) $\Longleftrightarrow x>\frac{5}{3}$.
(2) Consider $\frac{m-2}{m-1} \leqslant \frac{5}{3} \Leftrightarrow m \leqslant-\frac{1}{2}$. In this case, (I) has no solution.
$$
\text { Therefore, the solution is: } x>\frac{5}{3}, \text { if } m \geqslant 1 \text { or } -\frac{1}{2}<m<1.
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1 \text { or } -\frac{1}{2}<m<1.
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { In summary: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m \leqslant-\frac{1}{2}.
$$
$$
\text { Therefore, the solution is: }
$$
$$
x>\frac{5}{3}, \text { if } m \geqslant 1
$$
$$
\text { No solution, if } m