The inequality you've provided is:

$|2x + 3| < 7$

To solve this inequality, we follow these steps:

Step 1: Break it into two inequalities

Since the absolute value of an expression $|A| < B$ implies that $-B < A < B$, we can rewrite the inequality as:

$-7 < 2x + 3 < 7$

Step 2: Solve each part of the compound inequality

Solve the left inequality:

$-7 < 2x + 3$ Subtract 3 from both sides: $-7 - 3 < 2x \implies -10 < 2x$ Now divide by 2: $\frac{-10}{2} < x \implies -5 < x$

Solve the right inequality:

$2x + 3 < 7$ Subtract 3 from both sides: $2x < 7 - 3 \implies 2x < 4$ Now divide by 2: $x < \frac{4}{2} \implies x < 2$

Step 3: Combine the two results

We now have: $-5 < x < 2$

This means the solution to the inequality is: $x \in (-5, 2)$

Would you like further details or have any questions about this? Here are some related questions:

1. How would you solve if the inequality was $|2x + 3| > 7$?
2. What happens if the absolute value inequality includes a "less than or equal to" ($\leq$) sign?
3. How does solving absolute value inequalities differ from solving regular inequalities?
4. How do absolute value inequalities apply in real-world scenarios?
5. What if the inequality was $|2x + 3| = 7$?

Tip: Always split absolute value inequalities into two parts and remember that both the positive and negative aspects need to be considered!