If [x] is the greatest integer function and 2 | vedclass

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Question

(A) Given the equation: $2[2x - 5] - 1 = 7$ \Using the property $[x + n] = [x] + n$ for integer $n$,we have $[2x - 5] = [2x] - 5$ \Substituting this

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$\left[\frac{9}{2}, 5\right)$

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(A) Given the equation: $2[2x - 5] - 1 = 7$ \Using the property $[x + n] = [x] + n$ for integer $n$,we have $[2x - 5] = [2x] - 5$ \Substituting this into the equation: $2([2x] - 5) - 1 = 7$ \$2[2x] - 10 - 1 = 7$ \$2[2x] - 11 = 7$ \$2[2x] = 18$ \$[2x] = 9$ \By the definition of the greatest integer function,$[y] = n \Rightarrow n \leq y So,$9 \leq 2x Dividing by $2$,we get $\frac{9}{2} \leq x Thus,$x \in \left[\frac{9}{2}, 5ight)$

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

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