Write each of the following expressions without using absolute value. |z-7|-|z-9|, if z<7

Here's my thinking: If z<7, then z-7 is negative, and |z-7| is positive. So, with the understanding that z-7 is positive, the first part of this expression becomes:

7-z for z<7

Similarly: if z<7, then z-9 is negative and |z-9| is positive. Thus, - |z-9| is equivalent to (9-z).

|z-7|-|z-9|, if z<7 becomes (7-z) - (9-z) for z<7. Simplifying this, we get:

7 - z - 9 + z = - 2