Question

How do solve `5/x>3` and write the answer as a inequality and interval notation?

Answer 1

`5/3>x` or `color(blue)(x < 5/3)` and `(0,5/3)`

Explanation:

`(5/x>3)` as in equalities, can be multiplied on both sides by `x` then divided on both sides by `3`

`5 > 3x`

`5/3 > x` is the inequality.

The question gives us a hint in answering the interval notation part, because we can see right away that `x = 0` is undefined and so it must be excluded `color(red)((` as an endpoint.

Since there are no negative numbers given, we are not concerned about endpoints less than `0`.

We can also see from our solution above that `5/3 = x` cannot exist so 5/3 is an excluded `color(red))` endpoint.

Then the interval notation is `(0,5/3)`.

This means x can be `1` or any fraction between `0` and `5/3`, but it cannot be `0` or `5/3`.

Note that when you reverse components in the equality from one side to `color(blue)(the other side)` as in the answer above, it is necessary to REVERSE the sign of the inequality at the same time.