The equation possesses:

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

The equation ∣2ax−3∣+∣ax+1∣+∣5−ax∣=12|2ax-3|+|ax+1|+|5-ax|=\frac12 possesses: (1) an infinite number of real solutions for some a∈Ra\in\mathbb{R} (2) finitely many real solutions for some a∈Ra\in\mathbb{R} (3) no real solutions for some a∈Ra\in\mathbb{R} (4) no real solutions for all a∈Ra\in\mathbb{R}

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