Question

What is a value for `n` such that the compound inequality `-n < x< n` has no solutions?

Answer 1

Any `n <= 0` will work, e.g. `n=0`

Explanation:

Note that `<` is transitive. That is:

If `a < b` and `b < c` then `a < c`

In our example:

`-n < x` and `x < n" "` so `-n < n`

Adding `n` to both sides of this last inequality, we get:

`0 < 2n`

Then dividing both sides by `2` this becomes:

`0 < n`

So if we make this inequality false, then the given compound inequality must also be false, meaning that there is no suitable `x`.

So just put `n <= 0`, for example `n = 0`...

`0 < x < 0" "` has no solutions.