Question

Please help

1< |x– 2| < 5

Answer 1

`1 < |x -2|< 5\\1< |x-2| = |x-2| > 1\\-1 >x-2 \ , \ x-2<1\\1>x \ , \ x >3\\\\|x-2|<5 = -5 < x-2<5 = -3 <X<7\\\\Therefore , by \ merging \ overlapping \ intervals \\\\-3<x<1\quad \mathrm{or}\quad \:3<x<7`