Answer
$\left[ -\dfrac{7}{6},-\dfrac{5}{6} \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|-6x-6| \le 1
,$ use the definition of absolute value inequalities. Use the properties of inequalities to isolate the variable.
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 $\ge.$
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ (or $|x|\le c$ implies $-c\le x\le c$), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-1 \le -6x-6 \le 1
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-1+6 \le -6x-6+6 \le 1+6
\\\\
5 \le -6x \le 7
.\end{array}
Dividing by a negative number (and consequently reversing the sign), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{5}{-6} \ge \dfrac{-6x}{-6} \ge \dfrac{7}{-6}
\\\\
-\dfrac{5}{6} \ge x \ge -\dfrac{7}{6}
\\\\
-\dfrac{7}{6} \le x \le -\dfrac{5}{6}
.\end{array}
In interval notation, the solution set is $
\left[ -\dfrac{7}{6},-\dfrac{5}{6} \right]
.$
The colored graph is the graph of the solution set.