-4- I x+6 I =0 please solve with full steps?

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x+6=-4
impossible
no soln

-4-|x+6|=0
if x<-6 then -4-(-x-6)=0
-4+6+x=0
2+x=0
x=-2(Does not suit because x<-6)
if x>=-6 then -4-x-6=0
-10-x=0
x=10
answer: x=10

-4-1x+61=0
-1x=-61+4
-1x=-57
x=-57/-1
:. x=57

-4 - |x + 6| = 0
Just solve as if |x + 6| was x + 6
-4 - x + 6 = 0
(combine like terms [the -4 and 6])
2 - x = 0
(subtract 2 from both sides)
-x = - 2
x = 2

Now, assume that |x + 6| is -(x + 6)
-4 - -x + 6 = 0
Those two minus signs cancel out each other.
- 4 + x + 6 = 0
(combine like terms [-4 and 6])
2 + x = 0
(subtract 2 from both sides)
x = -2

So, x = 2 or -2.

| x + 6 | = 4
x + 6 = 4
x = - 2
OR
x + 6 = - 4
x = - 10
{ x : x = -2 , x = - 10, x Є R }

-4 - |x + 6| = 0
-|x + 6| = 4
|x + 6| = 4/-1
|x + 6| = -4 (<= impossible)
(no solution)