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

Sep 22, 2016

$\left(- \infty , 1\right)$ and $\left[3 , \infty\right)$

#### Explanation:

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

$a < x < b$ $\textcolor{w h i t e}{X X X X X X X} \left(a , b\right)$

or $a \le x < b$ $\textcolor{w h i t e}{X X X X X X} \left[a , b\right)$

or $a < x \le b$ $\textcolor{w h i t e}{X X X X X X} \left(a , b\right]$

or $a \le x \le b$ $\textcolor{w h i t e}{X X X X X X} \left[a , b\right]$

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 $x \ge 3$ and $x < 1$, this can be represented by

$- \infty < x < 1$ and $3 \le x < \infty$ i.e. $\left(- \infty , 1\right)$ and $\left[3 , \infty\right)$