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If $$S = \{a \in \mathbb{R} : |2a - 1| = 3[a] + 2\{a\}\}$$, where $$[t]$$ denotes the greatest integer less than or equal to $$t$$ and $$\{t\}$$ represents the fractional part of $$t$$, then $$72\sum_{a \in S} a$$ is equal to ______
Correct Answer: 18
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