Answer
$(\frac{-3}{4},\frac{17}{4})$
Work Step by Step
$|\frac{4x-7}{5}| \lt 2$
By the property, $|X| \lt a $ is equivalent to $-a \lt X \lt a$, the absolute value expression becomes,
$-2 \lt \frac{4x-7}{5} \lt 2$
$-10 \lt 4x-7 \lt 10$
$-10+7 \lt 4x-7+7 \lt 10+7$
$-3 \lt 4x\lt 17$
$\frac{-3}{4} \lt x \lt \frac{17}{4}$
Interval Notation : $(\frac{-3}{4},\frac{17}{4})$