Question

$$2 \lt b \lt 5 , | 2 a - b | \lt 3$$

Solve for b

$\left\{\begin{matrix}b\in \left(2a-3,5\right)\text{, }&a>\frac{5}{2}\text{ and }a<4\\b\in \left(2,2a+3\right)\text{, }&a>-\frac{1}{2}\text{ and }a<1\\b\in \left(2,5\right)\text{, }&a\geq 1\text{ and }a\leq \frac{5}{2}\end{matrix}\right.$

Solve for a

$a\in \left(\frac{b-3}{2},\frac{b+3}{2}\right)$
$b>2\text{ and }b<5$