$$\begin{cases}bx\ge5b-3\\ bx\le4b+3\end{cases}$$
$\left\{\begin{matrix}x\in \begin{bmatrix}4+\frac{3}{b},5-\frac{3}{b}\end{bmatrix}\text{, }&b<0\\x=4+\frac{3}{b}\text{; }x=5-\frac{3}{b}\text{, }&\left(b\geq 0\text{ and }b\leq 6\right)\text{ or }b\leq 0\\x\in \begin{bmatrix}5-\frac{3}{b},4+\frac{3}{b}\end{bmatrix}\text{, }&b>0\text{ and }b\leq 6\\x\in \mathrm{R}\text{, }&b=0\end{matrix}\right.$
$\left\{\begin{matrix}b\leq 3\text{, }&x=4\text{ or }x=5\\b\in \begin{bmatrix}\frac{3}{x-4},-\frac{3}{x-5}\end{bmatrix}\text{, }&x<4\\b\leq -\frac{3}{x-5}\text{, }&x>4\text{ and }x\leq \frac{9}{2}\\b\leq \frac{3}{x-4}\text{, }&x>\frac{9}{2}\text{ and }x<5\\b=\frac{3}{x-4}\text{, }&x\geq \frac{9}{2}\text{ or }x\leq 4\\b\in \begin{bmatrix}-\frac{3}{x-5},\frac{3}{x-4}\end{bmatrix}\text{, }&x>5\\b=-\frac{3}{x-5}\text{, }&x\leq \frac{9}{2}\text{ or }x\geq 5\end{matrix}\right.$