https://file.aiquickdraw.com/mathbot/file/1729051921994ozvnauu7.jpg

The inequality you provided is:

\[
|2x + 5| < 9
\]

### Step 1: Remove the absolute value

To solve the inequality, we break it into two cases, since the absolute value function generates two scenarios:

\[
-9 < 2x + 5 < 9
\]

### Step 2: Solve the inequality

We will now solve this as a compound inequality.

#### Left side:

\[
-9 < 2x + 5
\]
Subtract 5 from both sides:

\[
-14 < 2x
\]
Now, divide by 2:

\[
-7 < x
\]
or
\[
x > -7
\]

#### Right side:

\[
2x + 5 < 9
\]
Subtract 5 from both sides:

\[
2x < 4
\]
Now, divide by 2:

\[
x < 2
\]

### Step 3: Combine the results

The solution set is:

\[
-7 < x < 2
\]

In interval notation, the solution is:

\[
(-7, 2)
\]

### Conclusion:

Thus, the solution set is **not empty**. The correct answer is:

\[
A. \text{The solution set is } (-7, 2).
\]

Would you like more details or have any other questions?

Here are five questions to deepen your understanding:
1. How do you solve inequalities involving absolute values?
2. Why do we split absolute value inequalities into two cases?
3. Can you apply this method to solve other types of absolute value inequalities?
4. What changes if the inequality involves "greater than" instead of "less than"?
5. What would happen if the inequality had no solution?

**Tip:** Always check whether your final solution satisfies the original inequality by substituting values from the solution set.

Learn how to solve the absolute value inequality |2x + 5| < 9 using a step-by-step breakdown. This tutorial covers how to remove the absolute value and solve a compound inequality, providing the solution in interval notation: (-7, 2). Suitable for Grade 7 students.

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