Ans: (a) $x \neq -1$ (b) $-2$
-
$\begin{array}{rcl}
3 – x & > & \dfrac{7 – x}{2} \\
6 – 2x & > & 7 – x \\
-x & > & 1 \\
x & < & -1 \end{array}$Also,
$\begin{array}{rcl}
5 + x & > & 4 \\
x & > & -1
\end{array}$Therefore, $x < -1$ or $x > -1$.
Hence, the overall solution is $x \neq -1$.
- The greatest negative integer satisfying $(*)$ is $-2$.
