1. The problem involves solving an equation or inequality by breaking it into cases based on the value of $x$ being greater than 0 or less than 0. 2. When dealing with piecewise conditions, we analyze each case separately because the behavior of the function or expression may differ depending on the sign of $x$. 3. For $x > 0$, substitute this condition into the original equation or inequality and simplify accordingly. 4. For $x < 0$, substitute this condition and simplify separately. 5. Solve each simplified equation or inequality independently to find the solution sets for each case. 6. Finally, combine the solution sets from both cases to get the complete solution. 7. This method ensures accuracy by respecting the domain restrictions and the nature of the function or expression involved.