To solve the inequality \( |x - 2| < 9 \), we can rewrite it in terms of a double inequality. The expression \( |x - 2| < 9 \) means that the distance between \( x \) and 2 is less than 9.
We can express this as:
\[ -9 < x - 2 < 9 \]
Now, we can solve for \( x \) by adding 2 to all parts of the inequality:
\[ -9 + 2 < x < 9 + 2 \]
This simplifies to:
\[ -7 < x < 11 \]
Thus, the solution to the inequality \( |x - 2| < 9 \) is:
\[ \boxed{(-7, 11)} \]
This means that \( x \) can take any value between -7 and 11, not including -7 and 11 themselves.