− 4 < | | x − 1 | − 5 | < 4 {\displaystyle \ -4<||x-1|-5|<4}
− 4 < | x − 1 | − 5 | x − 1 | > 1 {\displaystyle {\begin{aligned}&-4<|x-1|-5\\&|x-1|>1\end{aligned}}}
| x − 1 | − 5 < 4 | x − 1 | < 9 − 9 < x − 1 < 9 {\displaystyle {\begin{aligned}&|x-1|-5<4\\&|x-1|<9\\&-9<x-1<9\\\end{aligned}}}
x − 1 > 1 x > 2 {\displaystyle {\begin{aligned}&x-1>1\\&x>2\\\end{aligned}}}
x − 1 < − 1 x < 0 {\displaystyle {\begin{aligned}&x-1<-1\\&x<0\\\end{aligned}}}
− 9 < x − 1 x > − 8 {\displaystyle {\begin{aligned}&-9<x-1\\&x>-8\\\end{aligned}}}
x − 1 < 9 x < 10 {\displaystyle {\begin{aligned}&x-1<9\\&x<10\\\end{aligned}}}
x < 0 ; x > 2 {\displaystyle \ x<0;x>2}
− 8 < x < 10 {\displaystyle \ -8<x<10}
− 8 < x < 0 2 < x < 10 {\displaystyle {\begin{aligned}&-8<x<0&2<x<10\end{aligned}}}
