Answer
$\left[ -101,-99 \right]$
Work Step by Step
Since for any $a\gt0$, $|x|\le a$ implies $-a\le x \le a$ then the solution to the given inequality, $
\left| 0.01x+1 \right|\le 0.01
,$ is
\begin{array}{l}\require{cancel}
-0.01\le 0.01x+1\le 0.01
\\\\
100(-0.01)\le 100(0.01x+1)\le 100(0.01)
\\\\
-1\le x+100\le 1
\\\\
-1-100\le x+100-100\le 1-100
\\\\
-101\le x\le -99
.\end{array}
Hence, the solution set is the interval $
\left[ -101,-99 \right]
.$
