To solve the inequality $|x + 7| < 9$, we need to break it down into two cases because the absolute value inequality $|A| < B$ implies that $-B < A < B$.

Step 1: Split the inequality

$-9 < x + 7 < 9$

Step 2: Solve for $x$

Now, subtract 7 from all three parts of the inequality:

$-9 - 7 < x < 9 - 7$

$-16 < x < 2$

Solution:

The solution to the inequality is $-16 < x < 2$, which means $x$ can take any value between -16 and 2 (but not including -16 and 2).

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Would you like more details or have any questions?

Here are five related questions to consider:

1. How do we solve inequalities involving $\leq$ or $\geq$ with absolute values?
2. What happens when the inequality symbol changes from $<$ to $>$?
3. How do you graph this solution on a number line?
4. Can you convert absolute value inequalities into compound inequalities in general?
5. How does solving absolute value equations differ from inequalities?

Tip: Always check your final solution by substituting values back into the original inequality.