Answer
The absolute value equation is $|x-2|=8$.
Work Step by Step
The given solutions are
$x=-6$ and $x=10$
Minimum value $=-6$
Maximum value $=10$
Halfway point $=2$.
Distance from halfway point $=8$.
Absolute value equation is
$\Rightarrow |x-$halfway point$|=$distance from halfway point
Substitute all the values.
$\Rightarrow |x-2|=8$
Check $x=-6$.
$\Rightarrow |-6-2|=8$
$\Rightarrow |-8|=8$
$\Rightarrow 8=8$
True.
Check $x=10$.
$\Rightarrow |10-2|=8$
$\Rightarrow |8|=8$
$\Rightarrow 8=8$
True.
Hence, the absolute value equation is $|x-2|=8$.
