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Let's solve each part step-by-step:

### Part (a) Solve the equation \( |2x - 3| = 5 \).

For an equation involving absolute values like \( |A| = B \), we set up two cases:

1. **Case 1**: \( 2x - 3 = 5 \)
   \[
   2x = 5 + 3 = 8
   \]
   \[
   x = \frac{8}{2} = 4
   \]

2. **Case 2**: \( 2x - 3 = -5 \)
   \[
   2x = -5 + 3 = -2
   \]
   \[
   x = \frac{-2}{2} = -1
   \]

Thus, the solutions to \( |2x - 3| = 5 \) are:
\[
x = 4 \quad \text{and} \quad x = -1
\]

---

### Part (b) Solve the inequality \( |2x - 3| < 5 \).

For an inequality involving absolute values like \( |A| < B \), we split it into:
\[
-5 < 2x - 3 < 5
\]

Solving this compound inequality:

1. **Left side**:
   \[
   -5 < 2x - 3
   \]
   \[
   -5 + 3 < 2x
   \]
   \[
   -2 < 2x
   \]
   \[
   -1 < x
   \]

2. **Right side**:
   \[
   2x - 3 < 5
   \]
   \[
   2x < 5 + 3
   \]
   \[
   2x < 8
   \]
   \[
   x < 4
   \]

Combining both parts, we get:
\[
-1 < x < 4
\]

---

### Part (c) Solve the inequality \( |2x - 3| > 5 \).

For an inequality involving absolute values like \( |A| > B \), we split it into two cases:

1. **Case 1**: \( 2x - 3 > 5 \)
   \[
   2x > 5 + 3
   \]
   \[
   2x > 8
   \]
   \[
   x > 4
   \]

2. **Case 2**: \( 2x - 3 < -5 \)
   \[
   2x < -5 + 3
   \]
   \[
   2x < -2
   \]
   \[
   x < -1
   \]

Thus, the solution to \( |2x - 3| > 5 \) is:
\[
x < -1 \quad \text{or} \quad x > 4
\]

---

### Summary of Solutions

1. **(a)** \( x = 4 \) and \( x = -1 \)
2. **(b)** \( -1 < x < 4 \)
3. **(c)** \( x < -1 \) or \( x > 4 \)

Would you like more details on any of these parts?

---

Here are five related questions for further practice:

1. How would you solve \( |3x + 2| = 7 \)?
2. What is the solution to \( |x - 5| < 2 \)?
3. How would you approach solving \( |4x - 1| > 3 \)?
4. How do absolute value inequalities change if the inequality is \( \geq \) or \( \leq \)?
5. What does it mean if an equation with an absolute value has no solution?

**Tip**: When solving absolute value equations or inequalities, always consider both the positive and negative cases.

Solve the equation and inequalities: a) |2x - 3| = 5, b) |2x - 3| < 5, c) |2x - 3| > 5.

Learn to solve the equation |2x - 3| = 5 and related inequalities |2x - 3| < 5 and |2x - 3| > 5. This guide covers the properties of absolute values in equations and inequalities, with a step-by-step breakdown. Suitable for students in Grades 9-11.

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