∣x−2∣<9

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.