In a Venn diagram representing three sets $A$, $B$, and $C$ within a universal set $U$, the eight disjoint regions have cardinalities related as follows:

• The region representing elements in all three sets has cardinality $x$.
• Each of the three regions representing elements in exactly two of the sets has cardinality $2x$.
• Each of the three regions representing elements in exactly one of the sets has cardinality $3x$.
• The region representing elements in none of the three sets has cardinality $4x$.

If the total number of elements in the universal set $U$ is 140, determine the cardinality of the set $(A \cup B) \setminus C$.