Answer
$\left[ -\dfrac{1}{2},\dfrac{35}{2} \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-1 \le \dfrac{2x-5}{6} \le 5
,$ use the properties of inequality.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
6(-1) \le 6\left( \dfrac{2x-5}{6} \right) \le 6(5)
\\\\
-6 \le 2x-5 \le 30
\\\\
-6+5 \le 2x-5+5 \le 30+5
\\\\
-1 \le 2x \le 35
\\\\
-\dfrac{1}{2} \le \dfrac{2x}{2} \le \dfrac{35}{2}
\\\\
-\dfrac{1}{2} \le x \le \dfrac{35}{2}
.\end{array}
In interval notation, the solution set is $
\left[ -\dfrac{1}{2},\dfrac{35}{2} \right]
.$
The red graph is the graph of the solution set.