1. **State the problem:** Solve the inequality $2\ln(|x-1|) - 2 > 0$. 2. **Rewrite the inequality:** Add 2 to both sides: $$2\ln(|x-1|) > 2$$ 3. **Divide both sides by 2:** $$\ln(|x-1|) > 1$$ 4. **Recall the property of logarithms:** For $\ln(a) > b$, where $a > 0$, this implies: $$a > e^b$$ 5. **Apply the property:** $$|x-1| > e^1 = e$$ 6. **Solve the absolute value inequality:** $$x-1 > e \quad \text{or} \quad x-1 < -e$$ 7. **Isolate $x$:** $$x > 1 + e \quad \text{or} \quad x < 1 - e$$ 8. **Domain consideration:** Since $|x-1|$ is inside the logarithm, $x \neq 1$ and the argument must be positive, which is satisfied by the solution. **Final answer:** $$x < 1 - e \quad \text{or} \quad x > 1 + e$$