Answer
The absolute value equation is $|x-5.5|=3.5$
Work Step by Step
The given solutions are
$x=2$ and $x=9$
Minimum value $=2$
Maximum value $=9$
Halfway point $=5.5$
Distance from halfway point $=3.5$
Absolute value equation is
$\Rightarrow |x-$halfway point$|=$distance from halfway point
Substitute all the values.
$\Rightarrow |x-5.5|=3.5$
Check $x=2$.
$\Rightarrow |2-5.5|=3.5$
$\Rightarrow |-3.5|=3.5$
$\Rightarrow 3.5=3.5$
True.
Check $x=9$.
$\Rightarrow |9-5.5|=3.5$
$\Rightarrow |3.5|=3.5$
$\Rightarrow 3.5=3.5$
True.
Hence, the absolute value equation is $|x-5.5|=3.5$
