1. Let's start by understanding what the absolute value means. 2. The absolute value of a number is the distance that number is from zero on the number line, regardless of direction. 3. This means absolute value is always positive or zero. 4. For example, |-3| means the distance of -3 from zero, which is 3. 5. Similarly, |3| means the distance of 3 from zero, which is also 3. 6. That's why |-3| becomes 3 and |3| remains 3 when taken outside the absolute value brackets. 7. So in general, for any number $x$, the absolute value $|x|$ is defined as: $$ |x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases} $$ 8. This piecewise definition shows the absolute value converts negative numbers to their positive counterpart and leaves positive numbers as they are. Final answer: The absolute value of a number is its distance from zero, so it is always non-negative, making |-3| = 3 and |3| = 3.