1. **State the problem:** Solve the inequality $$2|2x - 1| + 2 > 4$$. 2. **Isolate the absolute value expression:** Subtract 2 from both sides: $$2|2x - 1| > 2$$ 3. **Divide both sides by 2:** $$|2x - 1| > 1$$ 4. **Recall the definition of absolute value inequality:** For $$|A| > B$$ where $$B > 0$$, the solution is $$A < -B$$ or $$A > B$$. 5. **Apply this to our inequality:** $$2x - 1 < -1 \quad \text{or} \quad 2x - 1 > 1$$ 6. **Solve each inequality separately:** - For $$2x - 1 < -1$$: $$2x < 0$$ $$x < 0$$ - For $$2x - 1 > 1$$: $$2x > 2$$ $$x > 1$$ 7. **Combine the solution sets:** $$x < 0 \quad \text{or} \quad x > 1$$ 8. **Write the solution in interval notation:** $$(-\infty, 0) \cup (1, \infty)$$ **Final answer:** The solution set is $$(-\infty, 0) \cup (1, \infty)$$.