|x + 3| < 2

The given inequality is |x + 3| < 2.

Step 1: Understand the inequality This inequality is asking for all x values such that the absolute value of (x + 3) is less than 2.

Step 2: Break down the absolute value inequality An absolute value less than a number can be broken down into a compound inequality. |A| < B translates to -B < A < B. So, we can rewrite the inequality as -2 < x + 3 < 2.

Step 3: Solve the compound inequality We can solve this compound inequality by subtracting 3 from all parts of the inequality. This gives us -2 - 3 < x < 2 - 3, which simplifies to -5 < x < -1.

So, the solution to the inequality |x + 3| < 2 is -5 < x < -1.