Ans: (a) $\dfrac{-9}{2} < x < 3$ (b) $4$
- Consider the first inequality, we have
$\begin{array}{rcl}
3x+2 & > & \dfrac{4x-5}{2} \\
2(3x+2) & > & 4x-5 \\
6x+4 & > & 4x-5 \\
2x & > & -9 \\
x & > & \dfrac{-9}{2}
\end{array}$Consider the second inequality, we have
$\begin{array}{rcl}
3x-2 & < & 7 \\ 3x & < & 9 \\ x & < & 3 \end{array}$Therefore, the overall solution is $\dfrac{-9}{2} < x < 3$.
- There are $4$ negative integers satisfying $(*)$.
