To solve the inequality \( 5b + 4b < 23 \), first combine like terms:
\[ 9b < 23 \]
Next, divide both sides by 9:
\[ b < \frac{23}{9} \]
Now, simplify \(\frac{23}{9}\):
\[ b < 2.555\ldots \]
So the solution to the inequality is:
\[ b < \frac{23}{9} \quad \text{or} \quad b < 2.56 \text{ (approximately)} \]