Answer
$(-2,\frac{5}{2})$.
The graph is shown below.
Work Step by Step
The given compound inequality is
$6-5x\gt1-3x$ and $4x-3\gt x-9$.
Solve each inequality separately.
$\Rightarrow 6-5x\gt1-3x$ and $4x-3\gt x-9$.
$\Rightarrow 6\gt1-3x+5x$ and $4x-3-x\gt -9$.
$\Rightarrow 6\gt1+2x$ and $3x-3\gt -9$.
$\Rightarrow 6-1\gt2x$ and $3x\gt -9+3$.
$\Rightarrow 5\gt2x$ and $3x\gt -6$.
$\Rightarrow \frac{5}{2}\gt x$ and $x\gt -2$.
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.
$\frac{5}{2}\gt x$ as $(-\infty,\frac{5}{2})$ and $x\gt-2$ as $(-2,\infty)$
The intersection is
$(-\infty,\frac{5}{2})\cap(-2,\infty)=(-2,\frac{5}{2})$.
