Answer
If $a=5$ and $b=-2$, then $|5-(-2)|\gt|5|-|-2|$
If $a=5$ and $b=2$, then $|5-2|=|5|-|2|$
Work Step by Step
$|5-(-2)|\gt|5|-|-2|$
$|5+2|=|5|+|2|\gt5-2$
$7\gt3$
$|5-2|=|5|-|2|$
$3=|5|-|2|=5-2$
$3=3$
If $a$ and $b$ are both positive or both negative, then:
$|a-b|=|a|-|b|$ if $|a|\gt|b|$
or
$|a-b|=|b|-|a|$ if $|b|\gt|a|$. But, in this case $|a-b|\gt|a|-|b|$
If |a| and |b| have opposite signs then:
$|a-b|=|a|+|b|\gt|a|-|b|$
