Question

How do you solve `30 x<200` when `x` is a natural number?

Answer 1

Depending on your definition of a natural number, you can have
`0<x<20/3` or `0<=x<20/3`

Explanation:

Now, it depends on whether you think that 0 is a natural number or not.(I was taught that it isn't, but there are discussions about this. We will deal with this at the very end).

Assuming you meant that 0 isn't a natural number, we have:

`30x<200`
and
`x>0`

We solve the first inequality to get `x<20/3`

We now put the two inequalities together to get a compound inequality:
`0<x<20/3`
Now, if you want to include 0 as a natural number, you then have
`0<=x<20/3`