Answer
$(2,3)$.
Work Step by Step
The given compound inequality is
$2x+4\lt10$ and $3x-1\gt5$.
Solve each inequality separately.
First $2x+4\lt10$.
Subtract $4$ from both sides.
$\Rightarrow 2x+4-4\lt10-4$
Simplify.
$\Rightarrow 2x\lt6$
Divide both sides by $2$.
$\Rightarrow \frac{2x}{2}\lt\frac{6}{2}$
Simplify.
$\Rightarrow x\lt3$
Second $3x-1\gt 5$
Add $1$ to both sides.
$\Rightarrow 3x-1+1\gt5+1$
Simplify.
$\Rightarrow 3x\gt6$
Divide both sides by $3$.
$\Rightarrow \frac{3x}{3}\gt\frac{6}{3}$
Simplify.
$\Rightarrow x\gt2$
First graph the solution set of each inequality
We can write the solution set of the compound inequality.
$x\lt3$ as $(-\infty,3)$ and $x\gt2$ as $(2,\infty)$
Then take the intersection of the two solution sets.
The intersection is
$(-\infty,3)\cap(2,\infty)=(2,3)$.
The combined graph is shown below.
