The number of real solutions of the equation sin⁡ex=2x+2−x is

We know thatAM≥GM∴ 2x+2−x2≥2x×2−x⇒ 2x+2−x≥2But, sin  ex≤1Thus, sin⁡ex≠2x+2−x  for any x∈RHence, the given equation has no solution.