To solve the inequality $|x - 2.5| \leq 0.5$, we can proceed by breaking it down into two cases based on the absolute value definition.

The inequality $|x - 2.5| \leq 0.5$ means that the distance between $x$ and 2.5 is at most 0.5. Therefore, we can rewrite this as a compound inequality:

$-0.5 \leq x - 2.5 \leq 0.5$

Now, let's solve this inequality step-by-step:

1. Add 2.5 to each part of the inequality:

   $-0.5 + 2.5 \leq x \leq 0.5 + 2.5$

2. Simplify:

   $2 \leq x \leq 3$

So, the solution to the inequality $|x - 2.5| \leq 0.5$ is:

$2 \leq x \leq 3$

In interval notation, this can be written as:

$x \in [2, 3]$

Would you like more details on any step or have further questions?

Here are some related questions:

1. How would you solve a similar inequality if it was $|x - 4| < 2$?
2. Can you solve $|x + 1| \geq 3$ and interpret its solution?
3. How would the solution change if the inequality was $|x - 2.5| < 0.5$ instead of $\leq$?
4. How does the interval notation help in interpreting the solution set?
5. How do absolute values affect inequalities and solutions in general?

Tip: When solving absolute value inequalities, remember that $|A| \leq B$ translates to $-B \leq A \leq B$.