| | x − 2 | − 3 | > 1 {\displaystyle \ ||x-2|-3|>1}
| x − 2 | − 3 > 1 | x − 2 | > 4 {\displaystyle {\begin{aligned}&|x-2|-3>1\\&|x-2|>4\\\end{aligned}}}
| x − 2 | − 3 < − 1 | x − 2 | < 2 {\displaystyle {\begin{aligned}&|x-2|-3<-1\\&|x-2|<2\\\end{aligned}}}
( x − 2 ) > 4 x > 6 {\displaystyle {\begin{aligned}&(x-2)>4\\&x>6\\\end{aligned}}}
( x − 2 ) < − 4 x < − 2 {\displaystyle {\begin{aligned}&(x-2)<-4\\&x<-2\\\end{aligned}}}
x − 2 < 2 x < 4 {\displaystyle {\begin{aligned}&x-2<2\\&x<4\\\end{aligned}}}
x − 2 > − 2 x > 0 {\displaystyle {\begin{aligned}&x-2>-2\\&x>0\\\end{aligned}}}
0 < x < 4 {\displaystyle \ 0<x<4}
x < − 2 ; x > 6 {\displaystyle \ x<-2;x>6}
x < − 2 ; 0 < x < 4 ; x > 6 {\displaystyle {\begin{aligned}&x<-2;0<x<4;x>6\end{aligned}}}
