1. **State the problem:** Solve the inequality $|x-2| > 5$. 2. **Recall the definition of absolute value inequality:** For $|A| > B$ where $B > 0$, the solution is $A < -B$ or $A > B$. 3. **Apply the rule:** Here, $A = x-2$ and $B = 5$, so $$x - 2 < -5 \quad \text{or} \quad x - 2 > 5$$ 4. **Solve each inequality separately:** - For $x - 2 < -5$: $$x < -5 + 2$$ $$x < -3$$ - For $x - 2 > 5$: $$x > 5 + 2$$ $$x > 7$$ 5. **Write the final solution:** $$x < -3 \quad \text{or} \quad x > 7$$ This means $x$ is any number less than $-3$ or greater than $7$.