Tìm m để A = (m + 1; m + 4) giao B = [2m – 1; 3m] khác rỗng.

Để A ∩ B ≠ ∅ thì đầu tiên B ≠ ∅ hay 2m – 1 < 3m, tức là m > -1

Để A ∩ B ≠ ∅  thì \(\left[ \begin{array}{l}\left\{ \begin{array}{l}2m - 1 > m + 1\\2m - 1 < m + 4\end{array} \right.\\\left\{ \begin{array}{l}3m < m + 4\\3m > m + 1\end{array} \right.\end{array} \right.\)

⇔\(\left[ \begin{array}{l}\left\{ \begin{array}{l}m > 2\\m < 5\end{array} \right.\\\left\{ \begin{array}{l}m < 2\\m > \frac{1}{2}\end{array} \right.\end{array} \right.\)

⇔\(\left[ \begin{array}{l}2 < m < 5\\\frac{1}{2} < m < 2\end{array} \right.\)

Vậy m ∈ \(\left( {\frac{1}{2};2} \right) \cup \left( {2;5} \right)\)