Answer
$(-\infty,\infty)$.
The graph is shown below.
Work Step by Step
The given compound inequality is
$\Rightarrow 4x+3\lt-1$ or $2x-3\geq-11$.
Solve each inequality separately.
$\Rightarrow 4x+3\lt-1$ or $2x-3\geq-11$.
$\Rightarrow 4x\lt-1-3$ or $2x\geq-11+3$.
$\Rightarrow 4x\lt-4$ or $2x\geq-8$.
$\Rightarrow x\lt-1$ or $x\geq-4$.
First graph then take the union of the solution sets of the two inequalities.
The graph is shown in the image file.
We can write the compound inequality.
$x\lt-1$ as $(-\infty,-1)$ and $x\geq-4$ as $[-4,\infty)$
The union is
$(-\infty,-1)\cup[-4,\infty)=(-\infty,\infty)$.
