Solve the Absolute Value Inequality: |x+4| > 13

To solve the inequality $\left|x + 4\right| > 13$, we use the property of absolute values, which says that for $\left|a\right| > b$, it implies $a > b$ or $a < -b$.

Applying this to our problem, we have:

• $x + 4 > 13$ or $x + 4 < -13$.

Now, let's solve each inequality separately:

First inequality: $x + 4 > 13$

Subtract 4 from both sides to isolate $x$:

$x > 13 - 4$

$x > 9$

Second inequality: $x + 4 < -13$

Subtract 4 from both sides to isolate $x$:

$x < -13 - 4$

$x < -17$

Therefore, the solution to the inequality $\left|x + 4\right| > 13$ is $x > 9$ or $x < -17$.

The correct answer choice is:

• $x > 9$ or $x < -17$.