Answer
$(-\infty, -9)\cup (-3, +\infty)$
Work Step by Step
First, solve each simple inequality to have:
Inequality 1:
$x+9 \lt 0
\\x \lt -9$
Inequality 2:
$4x \gt -12
x \gt \frac{-12}{4}
\\x \gt -3$
This means that the given compound inequality is equivalent to $x \lt -9$ or $x \gt -3$.
Graph each simple inequality. (refer to the attached image below)
$x \lt -9$ includes all numbers to the left of -9
$\\x \gt -3$ includes all number to the right of -3.
The compound inequality involves the conjunction OR, which means that the solution set includes the combined elements of the two inequalities,
Thus, the solution set is:
$(-\infty, -9) \cup $(-3, +\infty)$
