If $[x]$ is greatest integer function and $2[2 x-5]-1=7$, then $x$ lies in

If $[x]$ is greatest integer function and $2[2 x-5]-1=7$, then $x$ lies in
  1. $\left[\frac{9}{2}, 5\right)$
  2. $\left[\frac{9}{2}, 5\right]$
  3. $\left(\frac{9}{2}, 5\right)$
  4. $\left(\frac{9}{2}, 5\right]$

Solution

$\begin{aligned} & 2[2 x-5]-1=7 \\ & \Rightarrow 2[2 x]-10-1=7 \\ & \Rightarrow[2 x]=9 \\ & \Rightarrow 9 \leq 2 x<10 \\ & x \in\left[\frac{9}{2}, 5\right)\end{aligned}$

Asked in: MHT CET 2022 (06 Aug Shift 2)

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