Answer
$(4,\infty)$.
Work Step by Step
The given compound inequality is
$5x+1\geq4x-2$ and $2x-3\gt5$.
Solve each inequality separately.
First
$\Rightarrow 5x+1\geq4x-2$
Add $-4x-1$ to both sides.
$\Rightarrow 5x+1-4x-1\geq4x-2-4x-1$
Simplify.
$\Rightarrow x\geq-3$
Second.
$\Rightarrow 2x-3\gt5$
Add $3$ to both sides.
$\Rightarrow 2x-3+3\gt5+3$
Simplify.
$\Rightarrow 2x\gt8$
Divide both sides by $2$.
$\Rightarrow \frac{2x}{2}\gt\frac{8}{2}$
Simplify.
$\Rightarrow x\gt4$
First graph then take the intersection of the two inequality.
We can write the compound inequality.
$x\geq-3$ as $[-3,\infty)$ and $x\gt4$ as $(4,\infty)$
The intersection is
$[-3,\infty)\cap(4,\infty)=(4,\infty)$.
