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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!

Learn how to solve the absolute value inequality |2x + 3| < 7 using a step-by-step approach. This guide breaks down the inequality into two linear inequalities and shows how to find the solution range for x, suitable for students in Grades 9-11.

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