solve for x where x is a real no.

Question

|x| + |x+1| + |x+3| = 4

First case,
x + x +1+x+3=4
3x+4=4
x=0

Second case
-(x+x+1+x+3)=4
-(3x+4)=4
3x+4=-4
3x= -8
x=-8/3

Am i right or wrong

Answer 1

if x >= 0
|x| + |x+1| + |x+3| = x+x+1+x+3 = 3x+4 = 4
so x = 0

if -1 <= x < 0
|x| + |x+1| + |x+3| = -x + x+1 + x+3 = x+4 = 4
x=0 does not meet the condition

If -3 <= x < -1
|x| + |x+1| + |x+3| = -x + -(x+1) + x+3 = -x+2 = 4
x = -2

If x < -3
|x| + |x+1| + |x+3| = -x + -(x+1) + -(x+3) = -3x-4 = 4
x = -8/3 but that does not fit the condition

so only 0 and -2 are solutions