Question

|x+2|<|3x+1|

Answer 1

Can anyone help me simplify?

Answer 2

let's draw the number line first

Answer 3

when x<-2
then both mods will open with a negative sign
-x-2<-3x-1
2x<1
or x<1/2
so answer is intersection of the two limits which is x<-2
when -2<x<-1/3
the right side mod will open with a negative
x+2<-3x-1
4x<-3
x<-3/4
this intersection with x<-1/3 will give x<-3/4
when x>-1/3
both mod will open with a positive
x+2<3x+1
1<2x
or x>1/2
intersection with x>-1/3 will give x>1/2
so our answer is x<-2, x<-3/4 and x>1/2
take union of all three we get
range of value of x
x< -3/4 and x>1/2