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.

Learn how to solve the absolute value inequality |2x - 5| < 11 with a detailed step-by-step solution. This problem demonstrates key algebraic concepts, including splitting inequalities into two cases. Suitable for students in Grades 9-10.

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