Question

How do you solve and write the following in interval notation: `x ≥ 3` and `x < 1`?

Answer 1

`(-oo,1)` and `[3,oo)`

Explanation:

In interval notation, a range of following types and these are written in interval notation as mentioned against them

`a < x < b` `color(white)(XXXXXXX)(a,b)`

or `a <= x < b` `color(white)(XXXXXX)[a,b)`

or `a < x <= b` `color(white)(XXXXXX)(a,b]`

or `a <= x <= b` `color(white)(XXXXXX)[a,b]`

Here `a` and `b` are lower and upper limits. Observe that symbols `(` and `)` denote that lower and upper limit are excluded and symbols `[` and `]` denote that lower and upper limit are included.

As we have `x>=3` and `x<1`, this can be represented by

`-oo < x < 1` and `3 <= x < oo` i.e. `(-oo,1)` and `[3,oo)`