3 < | x + 1 | < 6 3 < | x + 1 | a n d | x + 1 | < 6 x + 1 > 3 ; x + 1 < − 3 − 6 < x + 1 < 6 x + 1 > 3 ; x + 1 < − 3 x > 2 x < − 4 x > − 4 ; x > 2 − 6 < x + 1 < 6 − 6 < x + 1 − 7 < x x + 1 < 6 x < 5 − 7 < x < 5 2 < x < 5 ; − 7 < x < − 4 {\displaystyle {\begin{aligned}&3<|x+1|<6\\&3<|x+1|and|x+1|<6\\&{\color {blue}x+1>3;x+1<-3}&{\color {red}-6<x+1<6}\\&{\color {blue}x+1>3;x+1<-3}\\&\color {RoyalBlue}x>2\\&\color {Turquoise}x<-4\\&{\color {blue}x>-4;x>2}\\&\color {red}-6<x+1<6\\&\color {BrickRed}-6<x+1\\&\color {BrickRed}-7<x\\&\color {CarnationPink}x+1<6\\&\color {CarnationPink}x<5\\&\color {red}-7<x<5\\&\color {Purple}2<x<5;-7<x<-4\\\end{aligned}}}
