Answer
The absolute value of a difference will be the same as the difference of the absolute values when the two numbers being subtracted are the same.
(We can call these two numbers $a$ and $b$.)
$abs(a-b) = abs(a) - abs(b)$
Work Step by Step
The absolute values will also be the same when $a$ is positive, $b$ is positive, and $a > b > 0$.
If we let $a=3$ and $b=4$, then we have
$abs (3-4) = abs(3)-abs(4)$
$abs(-1) = 3-4$
$1 = -1$ (which is false)
Also, the difference will be the same when $a$ is negative, $b$ is negative, and $a < b < 0$.
If we let $a=-3$ and $b=-4$, then we have
$abs (-3--4) = abs(-3)-abs(-4)$
$abs(1) = 3-4$
$1 = -1$ (which is false)
