Less Than: Between

The inequality $\left|x\right| < 3$ asks for the numbers less than three steps from zero. Those are all the numbers between -3 and 3. Written as a chain:

$$-3 < x < 3$$

|x| < 3: the numbers within three steps of zero

When an absolute value is less than a number, it splits into a chain: $\left|u\right| < c$ becomes $-c < u < c$. With ≤ the ends are included, so $\left|x\right| \le 3$ becomes $-3 \le x \le 3$. A small absolute value means the number is close to zero, on either side.