Answer
$\text{the interval }
\left[ 1,\dfrac{11}{2} \right)
$
Work Step by Step
Using the properties of inequality, the solution to the given inequality, $
-1 \le \dfrac{2x-5}{3} \lt 2
,$ is
\begin{array}{l}\require{cancel}
-1\cdot3 \le \dfrac{2x-5}{3}\cdot3 \lt 2\cdot3
\\\\
-3 \le 2x-5 \lt 6
\\\\
-3+5 \le 2x-5+5 \lt 6+5
\\\\
2 \le 2x \lt 11
\\\\
\dfrac{2}{2} \le \dfrac{2}{2}x \lt \dfrac{11}{2}
\\\\
1 \le x \lt \dfrac{11}{2}
.\end{array}
In interval notation, the solution is $
\text{the interval }
\left[ 1,\dfrac{11}{2} \right)
.$