Answer
$[3,6)$.
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow -3\leq\frac{2x}{3}-5\lt-1$
Multiply the inequality by $3$.
$\Rightarrow -9\leq2x-15\lt-3$
Add $15$ to the inequality.
$\Rightarrow -9+15\leq2x-15+15\lt-3+15$
Add like terms.
$\Rightarrow 6\leq2x\lt12$
Divide the inequality by $2$.
$\Rightarrow 3\leq x\lt 6$
The interval notation is
$[3,6)$.
