Answer
The absolute value equation is $|x-13|=5$.
Work Step by Step
The given solutions are
$x=8$ and $x=18$
Minimum value $=8$
Maximum value $=18$
Halfway point $=13$.
Distance from halfway point $=5$.
Absolute value equation is
$\Rightarrow |x-$halfway point$|=$distance from halfway point
Substitute all the values.
$\Rightarrow |x-13|=5$
Check $x=8$.
$\Rightarrow |8-13|=5$
$\Rightarrow |-5|=5$
$\Rightarrow 5=5$
True.
Check $x=18$.
$\Rightarrow |18-13|=5$
$\Rightarrow |5|=5$
$\Rightarrow 5=5$
True.
Hence, the absolute value equation is $|x-13|=5$.
