MHB How can we rewrite a modulus function?

[Nousher Ahmed]

We can rewrite |x-3|<10 in the following way.

-10<x-3<10

But can rewrite |x-3|+|x+1|+|x|<10 in the following way?

-10<x-3+x+1+x<10.

If we cannot, will anybody please explain why we cannot?

 

[romsek]

You can't write it that way because it's not in general correct.

You can write it as a union of such rules though.

In this case it appears to be

$(x < -\dfrac 8 3) \cup (4 < x)$