Evaluate |-8 - 5|.

Step-by-step solution

1. 1

   Treat the bars as grouping symbols. Absolute value bars work like parentheses: everything inside must be simplified to a single number before the absolute value is applied. Splitting them as $|-8|-|5|$ would be wrong — that gives $8-5=3$, not the correct answer.

2. 2

   Simplify inside. Subtracting $5$ from $-8$ moves further in the negative direction:

   $-8-5=-13$

   Both quantities pull the same way, so the magnitudes add and the sign stays negative.

3. 3

   Apply the absolute value. The absolute value is the distance from $0$ on the number line, and distance is never negative:

   $|-13|=13$

4. 4

   State the answer.

   $|-8-5|=13$

   A negative input produced a positive output — that is the entire job of the absolute value.

5. 5

   Check the common wrong routes. Distributing the bars gives $8-5=3$ ✗, and dropping the minus early gives $|8-5|=3$ ✗. The correct value $13$ has a clear meaning: $-8$ and $5$ are $13$ units apart on the number line, and $|-8-5|=|-13|$ is exactly that distance, which is also how far $-13$ sits from the origin.