The problem asks to solve the absolute value inequality $|2x+5| < 9$.

1. Problem Description

The problem asks to solve the absolute value inequality $|2x+5| < 9$.

2. Solution Steps

The absolute value inequality $|2x+5| < 9$ can be rewritten as a compound inequality:

$$-9 < 2x+5 < 9$$

We can solve this by isolating $x$ in the middle. First, subtract $5$ from all three parts of the inequality:

$$-9 - 5 < 2x + 5 - 5 < 9 - 5$$

$$-14 < 2x < 4$$

Next, divide all three parts by $2$:

$$\frac{-14}{2} < \frac{2x}{2} < \frac{4}{2}$$

$$-7 < x < 2$$

3. Final Answer

The solution to the inequality is $-7 < x < 2$.