The inequality provided is:

$|x + 1| < 7$

To solve this absolute value inequality, we break it down into two inequalities based on the definition of absolute value:

$-7 < x + 1 < 7$

Step 1: Solve the inequality

We solve the two inequalities:

1. $-7 < x + 1$ Subtract 1 from both sides: $-7 - 1 < x \implies -8 < x$

2. $x + 1 < 7$ Subtract 1 from both sides: $x < 6$

Thus, the solution is:

$-8 < x < 6$

Step 2: Conclusion

The correct solution is the interval $(-8, 6)$. This corresponds to option A, where the inequality would be written as:

$-8 < x < 6$

Do you want any further details or have any questions?

Here are five related questions you might want to explore:

1. How do you graph an inequality like $-8 < x < 6$?
2. What changes if the inequality was $|x + 1| \leq 7$ instead of $|x + 1| < 7$?
3. How do we handle inequalities involving absolute value if they are greater than a constant?
4. What is the difference between strict inequalities ($<$) and non-strict inequalities ($\leq$)?
5. Can you solve compound inequalities and graph them?

Tip: When solving absolute value inequalities, always remember to split them into two inequalities, one representing the positive and the other the negative case.