Solve the inequation: `|1-(|x|/(1+|x|))|>=1/2`

Explanation

To solve the inequation \( |1 - \frac{|x|}{1 + |x|}| \geq \frac{1}{2} \), we will break it down into two cases based on the properties of absolute values.

### Step 1: Rewrite the Inequation
We start with the given inequation:
\[ |1 - \frac{|x|}{1 + |x|}| \geq \frac{1}{2} \]

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