Answer
$\varnothing$.
The graph is shown below.
Work Step by Step
The given compound inequality is
$4(1-x)\lt-6$ and $\frac{x-7}{5}\leq -2$.
Solve each inequality separately.
$\Rightarrow 4(1-x)\lt-6$ and $\frac{x-7}{5}\leq -2$.
$\Rightarrow 4-4x\lt-6$ and $x-7\leq -10$.
$\Rightarrow 4\lt-6+4x$ and $x\leq -10+7$.
$\Rightarrow 4+6\lt4x$ and $x\leq -3$.
$\Rightarrow 10\lt4x$ and $x\leq -3$.
$\Rightarrow \frac{10}{4}\lt x$ and $x\leq -3$.
$\Rightarrow \frac{5}{2}\lt x$ and $x\leq -3$.
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.
$\frac{5}{2}\lt x$ as $(\frac{5}{2},\infty)$ and $x\leq-3$ as $(-\infty,-3]$
The intersection is
$(-\infty,-3]\cap(\frac{5}{2},\infty)=\varnothing$.
