First solve

1/x ≤1=>x≥1

Then solve

1/x>-3=>x<-1/3

See the solution on the number line and you will find that there is no common solution which satisfies both the inequalities simultaneously.

So the solution is

-1/3 < x ≥ 1

That means the inequality holds good for all

x ≥ 1

And

-1/3 < x