Answer
$b\lt-3 $ or $b\geq 5$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 35\lt 7(2-b)$ or $\frac{1}{3}(15b-12) \geq 21$
Solve the first inequality.
$\Rightarrow 35\lt 7(2-b)$
Clear the parentheses.
$\Rightarrow 35\lt 14-7b$
Add $7b-35$ to each side.
$\Rightarrow 35+7b-35\lt 14-7b+7b-35$
Simplify.
$\Rightarrow 7b\lt -21$
Divide each side by $7$.
$\Rightarrow \frac{7b}{7}\lt \frac{-21}{7}$
Simplify.
$\Rightarrow b\lt -3$
Solve the second inequality.
$\Rightarrow \frac{1}{3}(15b-12) \geq 21$
Clear the parentheses.
$\Rightarrow 5b-4 \geq 21$
Add $4$ to each side.
$\Rightarrow 5b-4+4 \geq 21+4$
Simplify.
$\Rightarrow 5b \geq 25$
Divide each side by $5$.
$\Rightarrow \frac{5b}{5}\geq \frac{25}{5}$
Simplify.
$\Rightarrow b\geq 5$
Hence, the solution is $b\lt-3 $ or $b\geq 5$.
