Answer
$\left( -6.001,-5.999 \right)$
Work Step by Step
For any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a$. (The symbol $\lt$ may be replaced with $\le$.)
Using the concept above, the solutions to the given inequality, $
\left| x+6 \right|\lt0.001
,$ is
\begin{array}{l}\require{cancel}
-0.001\lt x+6\lt0.001
\\\\
-0.001-6\lt x\lt0.001-6
\\\\
-6.001\lt x\lt-5.999
.\end{array}
In interval notation, the solution set is $
\left( -6.001,-5.999 \right)
.$
