# Solve the following absolute value inequality. |x-2|>6

Solve the following absolute value inequality.
$|x-2|>6$
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Step 1
We can write the given function without absolute value as:
$|x-2|>6$
$x-2>6$ or $x-2<-6$
Step 2
Then we add 2 to both sides of both inequalities
$x-2>6\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}x-2<-6$
$x-2+2>6+2$ or $x-2+2<-6+2$
$x>8$ or $x<-4$
Result: $x>8$ or $x<-4$

Jeffrey Jordon