Answer
$(-\infty,\infty)$.
The graph of the solution set is given below.
Work Step by Step
The given compound inequality is
$\Rightarrow 5x+4\geq-11$ or $1-4x\geq9$.
First
$\Rightarrow 5x+4\geq-11$
Subtract $4$ from both sides.
$\Rightarrow 5x+4-4\geq-11-4$
Simplify.
$\Rightarrow 5x\geq-15$
Divide both sides by $5$.
$\Rightarrow \frac{5x}{5}\geq\frac{-15}{5}$
Simplify.
$\Rightarrow x\geq-3$
Second
$\Rightarrow 1-4x\geq9$
Subtract $1$ from both sides.
$\Rightarrow 1-4x-1\geq9-1$
Simplify.
$\Rightarrow -4x\geq8$
Divide both sides by $-4$ and change the sense of the inequality.
$\Rightarrow \frac{-4x}{-4}\leq\frac{8}{-4}$
Simplify.
$\Rightarrow x\leq-2$
First graph then take the union of the solution sets of the two inequalities.
We can write the compound inequality.
$x\geq-3$ as $[-3,\infty)$ or $x\leq -2$ as $(-\infty,-2]$
The union is
$[-3,\infty)\cup(-\infty,-2]=(-\infty,\infty)$.
The graph is shown below.
