Answer
Set notation:$\quad \{x|x\lt -20\}$
Interval notation:$\quad (-\infty, -20)$.
The graph is shown below.
Work Step by Step
Multiply both sides by $2$.
$2\cdot \frac{1}{2}(x-4)\gt 2\cdot (x+8) $
Simplify.
$x-4\gt 2x+16 $
Add $-16-x$ to both sides.
$x-4-16-x\gt 2x+16-16-x $
Simplify.
$-20\gt x $
The solution set is $\{x|x\lt -20\}$
or interval notation is $(-\infty, -20)$.
To graph, use a close parenthesis at $-20$ and shade the region to its left.
