Chapter 1 - Solving Linear Equations - 1.4 - Solving Absolute Value Equations - Exercises - Page 34: 54

always

Let $x=a-b$. Then we have $$b-a=-(a-b)=-x.$$ Because $|x|=|-x|$ we have $$|a-b|=|b-a|.$$ We conclude that $|a-b|$ is $\textbf{always}$ equal to $|b-a|$. Note: To prove that $|x|=|-x|$, consider $x>0$, then $x\leq 0$.