Step-by-Step Solution

Step-by-Step Solution

Step 1: Use the Bounded Absolute Value Property

For any positive constant $c > 0$, the inequality $|A| < c$ is mathematically equivalent to the double inequality:

Substituting $A = x^2 - 4$ and $c = 5$:

Step 2: Add 4 to All Three Parts

Step 3: Solve the Two Inequalities

This compound inequality consists of two simultaneous conditions:

1. Left Part: $x^2 > -1$ Since the square of any real number is always non-negative ($x^2 \ge 0$), this condition holds unconditionally for all $x \in \mathbb{R}$.
2. Right Part: $x^2 < 9$ Taking the square root: $$|x| < 3 \iff -3 < x < 3$$

Step 4: Find the Intersection

Intersecting $\mathbb{R}$ with $(-3, 3)$ yields: