Answer
The absolute value equation is $|x-34|=4$
Work Step by Step
Minimum value $=30$ inches
Maximum value $=38$ inches
Halfway point $=34$
Distance from halfway point $=4$
Absolute value equation is
$\Rightarrow |x-$halfway point$|=$distance from halfway point
Substitute all the values.
$\Rightarrow |x-(34)|=4$
Simplify.
$\Rightarrow |x-34|=4$
Check $x=30$.
$\Rightarrow |x-34|=4$
$\Rightarrow |30-34|=4$
$\Rightarrow |-4|=4$
$\Rightarrow 4=4$
True.
Check $x=38$.
$\Rightarrow |x-34|=4$
$\Rightarrow |38-34|=4$
$\Rightarrow |4|=4$
$\Rightarrow 4=4$
True.
Hence, the absolute value equation is $|x-34|=4$