For what values ​of x is true ${-(10^{10}})^{-j}\leq x \leq ({10^{10}})^{-j}$ whit $j=1,2,3...$ Can you give me any suggestions?
I understand that it is the same as
$x\leq|({10^{10}})^{-j}|$
but I don't know how to conclude

The bigger the j is, the smaller your x should be. Therefore, if the question is for which values of x, $x≤|(10^{10})^{−j}|$ is always true no matter the j you're choosing, then the answer will be $0\leq x\leq 0$. You can prove this answer is correct by showing the limit of $|(10^{10})^{−j}|$ when j goes to $\infty$ is a number closer and closer to 0.
