Answer
$(\frac{2}{5},2)$
Work Step by Step
$3 \lt 5x +1 \lt 11$
Using the properties of inequalities,
$3-1 \lt 5x +1 -1 \lt 11-1$
$2 \lt 5x \lt 10$
$\frac{2}{5} \lt \frac{5}{5}x \lt \frac{10}{5}$
$\frac{2}{5} \lt x \lt 2$
Interval Notation:$(\frac{2}{5},2)$