1. The problem is to express the relationship between the lengths of segments $AB$, $BC$, and $AC$ such that $|AB| = |BC| \neq |AC|$. 2. The absolute value notation $|XY|$ represents the length of the segment connecting points $X$ and $Y$. 3. Writing $|AB| = |BC|$ means the length of segment $AB$ is equal to the length of segment $BC$. 4. The notation $|AB| \neq |AC|$ means the length of segment $AB$ is not equal to the length of segment $AC$. 5. Combining these, $|AB| = |BC| \neq |AC|$ reads as "the length of $AB$ equals the length of $BC$, but both differ from the length of $AC$." 6. This is already the standard and correct mathematical notation to describe such a relationship between the segment lengths. 7. Therefore, you write the relationship exactly as $|AB| = |BC| \neq |AC|$.