1. **State the problem:** Simplify the expression $$(2x - 3y) + (y - 4z) - (z - 3x)$$. 2. **Apply the distributive property:** Remove parentheses carefully, remembering that the minus sign before the last parentheses changes the signs inside it. $$(2x - 3y) + (y - 4z) - (z - 3x) = 2x - 3y + y - 4z - z + 3x$$ 3. **Combine like terms:** Group terms with the same variables. For $x$: $$2x + 3x = 5x$$ For $y$: $$-3y + y = -2y$$ For $z$: $$-4z - z = -5z$$ 4. **Write the simplified expression:** $$5x - 2y - 5z$$ This is the simplified form of the original expression.