# Solve absolute value inequality : abs(x) > 3

Solve absolute value inequality : $|x|>3$
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Leonard Stokes
Step 1
the given absolute value inequality is:
$|x|>3$
we have to solve the given absolute value inequality.
Step 2
the given absolute value inequality is $|x|>3$
$|x|>3$
as we know that if $|x|>a$ then $x\in \left(-\mathrm{\infty },-a\right)\cup \left(a,\mathrm{\infty }\right)$
that implies if $|x|>a$ then $x<-a\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}x>a$
therefore if $|x|>3$ then $x<-3\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}x>3$
therefore the solution of the given absolute value inequality $|x|>3$ is $x<-3\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}x>3$.
the solution of the given absolute value inequality $|x|>3$ in interval notation is $x\in \left(-\mathrm{\infty },-3\right)\cup \left(3,\mathrm{\infty }\right)$