Question

|x|+|x-2|+|x-4|<5 x between?

Answer 1

the answer is 1<x<3 but how they made it?

Answer 2

|x|= x for x>=0
-x for x<0

|x-2|=x-2 for x >=2
-(x-2) for x<2

|x-4|=x-4 for x>=4
-(x-4) for x<4
so for
x>4
x+x-2+x-4=3x-6<5 ==> 3x<5+6
x<11/3

Answer 3

for x<0

Answer 4

-x-x+2-x+4<5
-3x+6<5
-3x<-1
x<1/3