# How do you solve and write the following in interval notation:  x <2 OR x > 1?

May 2, 2017

$x < 2 \text{ "OR" } x > 1 \Leftrightarrow \left(- \infty , \infty\right)$

#### Explanation:

$x < 2$ means $x$ can take any value less than two and interval notation, this means $\left(- \infty , 2\right)$, meaning that all numbers between $- \infty$ and $1$ are included and as $- \infty$ and $2$ are not included we have use small brackets. This forms one set of numbers, say $P$.

$x > 1$ means $x$ can take any value greater than one and interval notation tis means $\left(1 , \infty\right)$ , meaning that all numbers between $1$ and $\infty$ are included, but not $13$ and $\infty$. This forms another set of numbers, say $Q$.

Hence $x < 2 \text{ "OR" } x > 1$ represents the union of two sets $P$ and $Q$ i.e $P \cup Q$ or in other words $\left(- \infty , 2\right) \cup \left(1 , \infty\right)$.

Observe that $P \cup Q$ includes all the numbers from $- \infty$ to $\infty$ and hence $x < 2 \text{ "OR" } x > 1 \Leftrightarrow \left(- \infty , \infty\right)$