Answer
The absolute value equation is $|x-84.5|=10.5$
Work Step by Step
Minimum value $x=74$ miles per hour
Maximum value $x=95$ miles per hour
Halfway point $=84.5$
Distance from halfway point $=10.5$
Absolute value equation is
$\Rightarrow |x-$halfway point$|=$distance from halfway point
Substitute all the values.
$\Rightarrow |x-(84.5)|=10.5$
Simplify.
$\Rightarrow |x-84.5|=10.5$
Check $x=74$.
$\Rightarrow |x-84.5|=10.5$
$\Rightarrow |74-84.5|=10.5$
$\Rightarrow |-10.5|=10.5$
$\Rightarrow 10.5=10.5$
True.
Check $x=95$.
$\Rightarrow |x-84.5|=10.5$
$\Rightarrow |95-84.5|=10.5$
$\Rightarrow |10.5|=10.5$
$\Rightarrow 10.5=10.5$
True.
Hence, the absolute value equation is $|x-84.5|=10.5$
