The given inequality is $|2x - 3| < 5$.

To solve it, we need to remove the absolute value by breaking it into two inequalities:

$-5 < 2x - 3 < 5$

Step 1: Solve the left part

$-5 < 2x - 3$ Add 3 to both sides: $-5 + 3 < 2x$ $-2 < 2x$ Now, divide by 2: $-1 < x$

Step 2: Solve the right part

$2x - 3 < 5$ Add 3 to both sides: $2x < 8$ Now, divide by 2: $x < 4$

Final result:

The solution is: $-1 < x < 4$ In interval notation, the solution is: $(-1, 4)$

Would you like more details or explanations on any part?

Here are some related questions:

1. What happens if the inequality sign is reversed?
2. How do we handle absolute value inequalities with a "greater than" symbol?
3. Can you describe a real-life scenario where absolute value inequalities apply?
4. What is the graphical representation of this solution?
5. How would the solution change if the inequality had been $|2x - 3| \leq 5$?

Tip: Always remember to break absolute value inequalities into two cases—positive and negative—when solving.