1. **State the problem:** Make $x$ the subject of the formula given by $$4x - 6y = 2xz + 5u$$ 2. **Rewrite the equation:** Group all terms involving $x$ on one side: $$4x - 2xz = 6y + 5u$$ 3. **Factor out $x$ on the left side:** $$x(4 - 2z) = 6y + 5u$$ 4. **Isolate $x$ by dividing both sides by $(4 - 2z)$:** $$x = \frac{6y + 5u}{4 - 2z}$$ 5. **Show cancellation if possible:** $$x = \frac{6y + 5u}{\cancel{2}(2 - z)}$$ Since $4 - 2z = 2(2 - z)$, we can write: $$x = \frac{6y + 5u}{2(2 - z)}$$ This is the expression for $x$ in terms of $y$, $u$, and $z$. **Final answer:** $$x = \frac{6y + 5u}{2(2 - z)}$$