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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.

Solve |2x - 3| < 5 and give your answer as an interval.

Learn how to solve the absolute value inequality |2x - 3| < 5 step-by-step. This problem demonstrates how to break absolute value inequalities into two linear inequalities and solve for x. Suitable for students in Grades 8-10.

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