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The solution ...

Question

The solution of $x [x] - x^{2} - 5 [x] + 5 x \geq 0$ (where $[x]$ stands for the greatest integer less than or equal to $x$ ) lies in the interval

[5, 6)

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[6, 7)

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[5, \infty)

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(- \infty, 5)

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Solution

The correct option is C $(- \infty, 5)$
$(x - 5) [x] - (x - 5) x > 0$
$(x - 5) ([x] - x) > 0$
$∴ [x] - x < 0$
$\Rightarrow x - 5 < 0$
$x < 5$
$∴ x \in (- \infty, 5)$

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