The inequality \(|9 - 2x| < 1\) can be rewritten as two separate inequalities:

1. \(9 - 2x < 1\)

2. \(9 - 2x > -1\)

Solving the first inequality:

\(9 - 2x < 1\)

Subtract 9 from both sides:

\(-2x < -8\)

Divide by -2 (and reverse the inequality sign):

\(x > 4\)

Solving the second inequality:

\(9 - 2x > -1\)

Subtract 9 from both sides:

\(-2x > -10\)

Divide by -2 (and reverse the inequality sign):

\(x < 5\)

Combining both results, we get:

\(4 < x < 5\)