\input amstex
\font\amssy=msam10

\def\leqslant{\mathrel{\hbox{\amssy\char54}}}
\def\geqslant{\mathrel{\hbox{\amssy\char62}}}

\def\eqslantless{\mathrel{\hbox{\amssy\char48}}}
\def\eqslantgtr{\mathrel{\hbox{\amssy\char49}}}

$$g(x)=\biggl||x|-4\biggr|=\cases
x-4,&x\geqslant 0\land |x|-4\geqslant 0,\cr
-(x-4),&x\geqslant 0\land |x|-4<0,\cr
(-x)-4,&x<0\land |x|-4\geqslant 0,\cr
-\bigl((-x)-4\bigr),&x<0\land |x|-4<0.
\endcases$$
\bye