Answer
$v\leq 2$.
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 4v+9\leq 5$ or $-3v \geq -6$
Solve the first inequality.
$\Rightarrow 4v+9\leq 5$
Subtract $9$ from each side.
$\Rightarrow 4v+9-9\leq 5-9$
Simplify.
$\Rightarrow 4v\leq -4$
Divide each side by $4$.
$\Rightarrow \frac{4v}{4}\leq \frac{-4}{4}$
Simplify.
$\Rightarrow v\leq -1$
Solve the second inequality.
$\Rightarrow -3v \geq -6$
Divide each side by $-3$. Reverse the inequality symbol.
$\Rightarrow \frac{-3v}{-3}\leq \frac{-6}{-3}$
Simplify.
$\Rightarrow v\leq 2$
Merge the overlapping interval.
$\Rightarrow v\leq 2$
Hence, the solution is $v\leq 2$.
