To solve the inequality $|2x - 5| < 11$, we need to split it into two cases based on the definition of absolute value:

Case 1: Positive scenario

$2x - 5 < 11$

1. Add 5 to both sides: $2x < 16$

2. Divide by 2: $x < 8$

Case 2: Negative scenario

$-(2x - 5) < 11$

This simplifies to: $2x - 5 > -11$

1. Add 5 to both sides: $2x > -6$

2. Divide by 2: $x > -3$

Final solution:

Combining both cases, we get: $-3 < x < 8$

Thus, the solution is $x \in (-3, 8)$.

Would you like more details on any step? Here are some related questions to deepen understanding:

1. How do we solve absolute value equations?
2. What happens when we solve an absolute value inequality involving "greater than"?
3. How do you graph the solution $-3 < x < 8$?
4. What are the implications of dividing inequalities by negative numbers?
5. Can we use a different method to solve this inequality?

Tip: Always remember that solving absolute value inequalities involves splitting the expression into two cases: one for the positive scenario and one for the negative.