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

It depends on how you interpret the final phrase "with $j=1,2,3,\cdots.$" If it means just pick one of them then your answer is OK. If it means it should be true for every $k$ you need to intersect all the answers.
