Answer
The absolute value equation is $|x+7.5|=2.5$
Work Step by Step
The given solutions are
$x=-10$ and $x=-5$
Minimum value $=-10$
Maximum value $=-5$
Halfway point $=-7.5$
Distance from halfway point $=2.5$
Absolute value equation is
$\Rightarrow |x-$halfway point$|=$distance from halfway point
Substitute all the values.
$\Rightarrow |x-(-7.5)|=2.5$
Simplify.
$\Rightarrow |x+7.5|=2.5$
Check $x=-10$.
$\Rightarrow |-10+7.5|=2.5$
$\Rightarrow |-2.5|=2.5$
$\Rightarrow 2.5=2.5$
True.
Check $x=-5$.
$\Rightarrow |-5+7.5|=2.5$
$\Rightarrow |2.5|=2.5$
$\Rightarrow 2.5=2.5$
True.
Hence, the absolute value equation is $|x+7.5|=2.5$
