Let's solve the given inequality step by step:

The inequality is:

$5 |x + 1| < 45$

Step 1: Isolate the absolute value.

To simplify the inequality, divide both sides by 5:

$|x + 1| < 9$

Step 2: Solve the absolute value inequality.

For the inequality $|x + 1| < 9$, this means that the expression inside the absolute value, $x + 1$, is between -9 and 9. Therefore, we can rewrite this as:

$-9 < x + 1 < 9$

Step 3: Solve for $x$.

Subtract 1 from all parts of the inequality:

$-9 - 1 < x < 9 - 1$

This simplifies to:

$-10 < x < 8$

Step 4: Match the solution with the given choices.

The correct answer is:

$-10 < x < 8$

Thus, the correct option is the fourth one: $-10 < x < 8$.

Would you like further clarification on any step?

Here are five related questions to explore:

1. How do you solve absolute value inequalities involving "greater than"?
2. What are the properties of absolute value functions in inequalities?
3. Can you explain how to graph the solution $-10 < x < 8$ on a number line?
4. How would the solution change if the inequality had $|x + 1| \leq 9$?
5. How can absolute value inequalities be applied in real-world problems?

Tip: When solving absolute value inequalities, always remember to break them into two separate inequalities (one for the positive and one for the negative case).