Answer
$\frac{1}{3}\lt b \lt 3$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 4|-3b+5|-9\lt 7$
Add $9$ to each side.
$\Rightarrow 4|-3b+5|-9+9\lt 7+9$
Simplify.
$\Rightarrow 4|-3b+5|\lt 16$
Divide each side by $4$.
$\Rightarrow \frac{4|-3b+5|}{4}\lt \frac{16}{4}$
Simplify.
$\Rightarrow |-3b+5|\lt 4$
Write a compound inequality.
$\Rightarrow -3b+5\lt 4$ and $-3b+5\gt -4$
Subtract $5$ from each side.
$\Rightarrow -3b+5-5\lt 4-5$ and $-3b+5-5\gt -4-5$
Simplify.
$\Rightarrow -3b\lt -1$ and $-3b\gt -9$
Divide each side by $-3$. Reverse the inequality symbol.
$\Rightarrow \frac{-3b}{-3}\gt \frac{-1}{-3}$ and $\frac{-3b}{-3}\lt \frac{-9}{-3}$
Simplify.
$\Rightarrow b\gt \frac{1}{3}$ and $b\lt 3$
Hence, the solution is $\frac{1}{3}\lt b \lt 3$.
