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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.

Learn how to solve the absolute value inequality |x + 1| < 7 by breaking it down into two inequalities and solving them step-by-step. This problem is ideal for students in Grades 7-10.

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