The inequality you're trying to solve is:

$|7x + 2| < 9$

To solve absolute value inequalities, we need to split the inequality into two cases:

1. $7x + 2 < 9$
2. $7x + 2 > -9$

Case 1: $7x + 2 < 9$

Subtract 2 from both sides:

$7x < 7$

Now divide by 7:

$x < 1$

Case 2: $7x + 2 > -9$

Subtract 2 from both sides:

$7x > -11$

Now divide by 7:

$x > -\frac{11}{7}$

Final Solution:

Combining both results, we get:

$-\frac{11}{7} < x < 1$

In interval notation, the solution is:

$\left( -\frac{11}{7}, 1 \right)$

Would you like a more detailed explanation or have any other questions? Here are some related topics you may want to explore:

1. What happens when you solve absolute value inequalities with $\geq$ or $\leq$?
2. How do you handle absolute value equations instead of inequalities?
3. What is the difference between strict and non-strict inequalities?
4. How can you solve absolute value inequalities with multiple terms inside?
5. Can absolute value inequalities be represented graphically, and how?

Tip: Always remember to isolate the absolute value expression before splitting into two cases.