Question

solve the following inequality algebraically.
$|x + 4| > 9$

Explanation:

Step1: Apply absolute value rule

For $|A| > B$, this splits into $A > B$ or $A < -B$.
So we get:
$x + 4 > 9$ or $x + 4 < -9$

Step2: Solve first inequality

Subtract 4 from both sides.
$x + 4 - 4 > 9 - 4$
$x > 5$

Step3: Solve second inequality

Subtract 4 from both sides.
$x + 4 - 4 < -9 - 4$
$x < -13$

Answer:

$x < -13$ or $x > 5$ (in interval notation: $(-\infty, -13) \cup (5, \infty)$)