write the solution set of inequation: `|1/(x-2)|` `<4,x!=4.`

Explanation

To solve the inequality \(\left| \frac{1}{x-2} \right| < 4\) with the condition \(x \neq 4\), we can break it down into two cases based on the definition of absolute value.

### Step 1: Remove the Absolute Value
The inequality \(\left| \frac{1}{x-2} \right| < 4\) can be rewritten as two separate inequalities:
\[ -\frac{1}{x-2} < 4 \quad \text{and} \quad \frac{1}{x-2} < 4 \]

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