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.