Answer
$(-\infty,-3]$.
The graph is shown below.
Work Step by Step
The given compound inequality is
$2x+1\gt 4x-3$ and $x-1\geq 3x+5$.
Solve each inequality separately.
$\Rightarrow 2x+1\gt 4x-3$ and $x-1\geq 3x+5$.
$\Rightarrow 2x+1+3\gt 4x$ and $x-1-5\geq 3x$.
$\Rightarrow 2x+4\gt 4x$ and $x-6\geq 3x$.
$\Rightarrow 4\gt 4x-2x$ and $-6\geq 3x-x$.
$\Rightarrow 4\gt 2x$ and $-6\geq 2x$.
$\Rightarrow 2\gt x$ and $-3\geq x$.
First graph then take the intersection of the solution sets of the two inequalities.
The graph is shown in the image file.
We can write the compound inequality.
$2\gt x$ as $(-\infty,2)$ and $-3\geq x$ as $(-\infty,-3]$
The intersection is
$(-\infty,2)\cap(-\infty,-3]=(-\infty,-3]$.
