Solve absolute value inequality : abs(x) > 3

Step 1
the given absolute value inequality is:
${\displaystyle \left|x\right|>3}$
we have to solve the given absolute value inequality.
Step 2
the given absolute value inequality is ${\displaystyle \left|x\right|>3}$
${\displaystyle \left|x\right|>3}$
as we know that if ${\displaystyle \left|x\right|>a}$ then ${\displaystyle x\in (-\mathrm{\infty },-a)\cup (a,\mathrm{\infty })}$
that implies if ${\displaystyle \left|x\right|>a}$ then ${\displaystyle x<-a\text{or}x>a}$
therefore if ${\displaystyle \left|x\right|>3}$ then ${\displaystyle x<-3\text{or}x>3}$
therefore the solution of the given absolute value inequality ${\displaystyle \left|x\right|>3}$ is ${\displaystyle x<-3\text{or}x>3}$.
the solution of the given absolute value inequality ${\displaystyle \left|x\right|>3}$ in interval notation is ${\displaystyle x\in (-\mathrm{\infty },-3)\cup (3,\mathrm{\infty })}$