Answer
$-2 \lt x \lt 1$
$\\\\$Graphing the inequality gives:
Work Step by Step
Multiply 3 to each part to have:
$\\\\-1(3) \lt \dfrac{-2x-1}{3} \cdot 3 \lt 1(3)
\\\\-3 \lt -2x-1 \lt 3$
$\\\\\\$Add $1$ to each part to have:
$\\\\-3+1 \lt -2x-1+1 \lt 3+1
\\\\-2 \lt -2x \lt 4$
$\\\\\\$Divide -2 to each part (note that this will flip the inequality symbol) to have:
$\\\\1 \gt x \gt -2
\\\\-2 \lt x \lt 1$