Let's simplify the expression:

$3x - 4y + z - 2z + x - y$

Step by step:

1. Combine the like terms:
   • For the $x$-terms: $3x + x = 4x$
   • For the $y$-terms: $-4y - y = -5y$
   • For the $z$-terms: $z - 2z = -z$

Now, the expression becomes:

$4x - 5y - z$

So the simplified expression is:

$4x - 5y - z$

Would you like more details or have any questions about this?

Here are some related questions:

1. What is the value of this expression when $x = 2$, $y = 3$, and $z = 1$?
2. How do you factorize an expression like $4x - 5y - z$?
3. How do you solve a system of equations involving similar expressions?
4. What are the properties of like terms in algebra?
5. How can you simplify an expression involving polynomials?

Tip: Always combine like terms first when simplifying algebraic expressions!