The question is asking for the value of $|a - b|$, given that $a < b$.

Solution:

• The absolute value function $|x|$ is defined as: \begin{cases} x & \text{if } x \geq 0, \\ -x & \text{if } x < 0. \end{cases}$$
• Since $a < b$, it means $a - b$ is negative, and thus: $|a - b| = -(a - b) = b - a.$

So, the correct answer is $b - a$, which you have selected.

Would you like a more detailed explanation or any further clarifications? Here are some related questions:

1. How is the absolute value function used in inequalities?
2. What are the general properties of the absolute value function?
3. How would this question change if $a > b$?
4. Can the absolute value of a difference between two numbers ever be negative?
5. How can absolute value be applied in real-world scenarios?

Tip: When working with absolute values, always consider the sign of the expression inside the absolute value to determine whether it needs to be negated or left as is.