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We are given the inequality \( 3 > |b - 5| \). 

### Step-by-step solution:

1. **Definition of absolute value inequality**:
   For any \( |x| < c \), where \( c > 0 \), this means:
   \[
   -c < x < c
   \]
   So in this case, we can split the inequality \( 3 > |b - 5| \) into two parts:
   \[
   -3 < b - 5 < 3
   \]

2. **Solving for \( b \)**:
   - First, solve the left inequality:
     \[
     -3 < b - 5
     \]
     Add 5 to both sides:
     \[
     2 < b
     \]
   
   - Now, solve the right inequality:
     \[
     b - 5 < 3
     \]
     Add 5 to both sides:
     \[
     b < 8
     \]

3. **Combined inequality**:
   Now, combining both results, we get:
   \[
   2 < b < 8
   \]
   So, the solution is \( b \in (2, 8) \).

### Graphing the solution:

- The solution represents an open interval between 2 and 8. On a number line:
  - Open circles at \( b = 2 \) and \( b = 8 \) (since these are not included in the solution).
  - A line segment between 2 and 8.

Would you like me to add further details or explanations on this solution?

### Five related questions:
1. How do we handle inequalities involving absolute values?
2. What are the different methods to solve absolute value inequalities?
3. How would the solution change if the inequality was \( 3 \geq |b - 5| \)?
4. Can you apply this technique to solve other inequalities, such as \( |b + 7| < 10 \)?
5. How would we graph the solution if the inequality involved \( \leq \) or \( \geq \)?

### Tip:
When solving absolute value inequalities, always split them into two cases—one positive and one negative—and solve each case separately.

Solve for b and graph the solution: 3 > |b - 5|.

Learn how to solve and graph the absolute value inequality 3 > |b - 5| with a step-by-step breakdown. This problem involves the concepts of absolute value inequalities and algebraic manipulation, making it suitable for students in Grades 8-10.

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