MHB Absolute Value: Solve for x | MHB

[Petrus]

Hello MHB,
solve $$||x|-2|+|x+1|=3$$
and we find that $$x=0,-2,2,-1$$
I got problem to find the 'case',

Regards,
$$|\rangle$$

 

[I like Serena]

Hello MHB,
solve $$||x|-2|+|x+1|=3$$
and we find that $$x=0,-2,2,-1$$
I got problem to find the 'case',

Regards,
$$|\rangle$$

That doesn't look like the right solution...

Talking about cases, what if x<-2? Or -2<x<-1? And what about -1<x<0? Or perhaps 0<x<2? And x>2?

 

[Petrus]

That doesn't look like the right solution...

Talking about cases, what if x<-2? Or -2<x<-1? And what about -1<x<0? Or perhaps 0<x<2? And x>2?

I don't mean those are the answer, but those are the point we should check $$\geq$$ or $$\leq$$, I hope you did understand.
Can I also check this one insted of -1<x<0
-2<x<0?

Regards,
$$|\rangle$$

 

[I like Serena]

I don't mean those are the answer, but those are the point we should check $$\geq$$ or $$\leq$$, I hope you did understand.
Can I also check this one insted of -1<x<0
-2<x<0?

Sure you can. It's just that |x+1| does something funny at x=-1.

 

[Petrus]

Sure you can. It's just that |x+1| does something funny at x=-1.

Thanks, got the correct answer now :)
Regards,
$$|\rangle$$