## College Algebra (11th Edition)

$\left[ -101,-99 \right]$
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 $\left[ -101,-99 \right] .$