Absolute Value Inequality: Determining Outcomes for |x-5| > 11

To solve the inequality $\left|x-5\right| > 11$, we first apply the property of absolute values:

• If $\left|A\right| > B$, then $A > B$ or $A < -B$.

Therefore, for $\left|x-5\right| > 11$, we have two cases to consider:

• Case 1: $x-5 > 11$
• Case 2: $x-5 < -11$

Let's solve each case separately:

Case 1: $x-5 > 11$

Add 5 to both sides to isolate $x$:
$x > 11 + 5$

This simplifies to:

$x > 16$

Case 2: $x-5 < -11$

Add 5 to both sides to isolate $x$:
$x < -11 + 5$

This simplifies to:

$x < -6$

Thus, the solution to the inequality is:

$x > 16$ or $x < -6$

Comparing this result with the given answer choices, the correct one is:

$x>16$ o $x<-6$

Therefore, the solution to the problem is $x > 16$ or $x < -6$.