Chapter 2 - Section 2.1 - Introduction to Integers - Exercise Set - Page 105: 79

$-|-2|\gt -|-10|$

If $a-b \lt 0$, then $a \lt b;$ If $a-b \gt 0$, then $a \gt b;$ If $a-b = 0$, then $a=b;$ In this problem, $a=-|-2|=2,$ $b=-|-10|=-10,$ Since $a-b=2-(-10)=2+10=12\gt0,$ Then $a\gt b,$ Therefore, $-|-2|\gt -|-10|$