How do you write the following in interval notation: x>2 OR 5>x?

Jan 22, 2018

$\textcolor{b l u e}{\forall x \in \mathbb{R}}$

Using Interval Notation

color(blue)[(-oo, +oo)

Explanation:

Given the inequality:

$\textcolor{red}{x > 2 \mathmr{and} 5 > x}$

Write color(green)(5>x as color(green)(x < 5 after switching sides

So we get,

$\textcolor{red}{x > 2 \mathmr{and} x < 5}$

This is $T r u e$

If we combine both the results, we get

$\textcolor{b l u e}{\forall x \in \mathbb{R}}$

Using Interval Notation we can write

color(blue)[(-oo, +oo)

Analyze the graph below to view the behavior of the inequality: