## Precalculus: Mathematics for Calculus, 7th Edition

$\left( -6.001,-5.999 \right)$
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 $\left( -6.001,-5.999 \right) .$