Solve |x+2| < 3: Absolute Value Inequality Analysis

To solve the inequality $|x + 2| < 3$, we will apply the property of absolute values by rewriting it without the absolute value sign as follows:

Step 1: Transform the absolute value inequality
Using the rule $|A| < B$ implies $-B < A < B$, we write

$-3 < x + 2 < 3$.

Step 2: Solve this compound inequality. We do this by isolating $x$ as follows:

• Subtract 2 from all parts: $-3 - 2 < x + 2 - 2 < 3 - 2$.
• This simplifies to: $-5 < x < 1$.

Thus, the inequality $|x + 2| < 3$ is solved as $-5 < x < 1$.

The correct solution is contained in choice 3: $-5 < x < 1$.