Problem Solving

I am little confused about substituting a negative number in a modulus function..Please tell me whats wrong in my approach

|X-Z| + |X|

Now if both X and Z are negative and Z < X ...How should I substitute the negative values for the X and Y

I do the following.

|-X - (-Z) | + |-X|

= |Z-X| + |X|

= Z- X +X (Taking away the modulus as the negative sign has already been assigned to the variables)

= Z

But actually the answer should be -Z ... Please let me know the right approach

Thanks,
Sai