Answer
$d\lt -8 $ or $d\gt -\frac{1}{2}$
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 2d+7\lt -9$ or $4d-1 \gt -3$
Solve the first inequality.
$\Rightarrow 2d+7\lt -9$
Subtract $7$ from each side.
$\Rightarrow 2d+7-7\lt -9-7$
Simplify.
$\Rightarrow 2d\lt -16$
Divide each side by $2$.
$\Rightarrow \frac{2d}{2}\lt \frac{-16}{2}$
Simplify.
$\Rightarrow d\lt -8$
Solve the second inequality.
$\Rightarrow 4d-1 \gt -3$
Add $1$ to each side.
$\Rightarrow 4d-1+1 \gt -3+1$
Simplify.
$\Rightarrow 4d\gt -2$
Divide each side by $4$.
$\Rightarrow \frac{4d}{4}\gt \frac{-2}{4}$
Simplify.
$\Rightarrow d\gt -\frac{1}{2}$
Hence, the solution is $d\lt -8 $ or $d\gt -\frac{1}{2}$.
