Algebra 1

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 $b$.) $abs(a-b) = abs(a) - abs(b)$
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)