The number of solutions of $| [x] - 2 x | = 4$ where [x] is the greatest integer is

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Solution

The correct option is B
4

$I f x = n ϵ Z, | n - 2 n | = 4 \Rightarrow n \pm 4$

If x = n + K where 0 < K < 1 then $| n - 2 (n + k) | = 4$ it is possible if $K = \frac{1}{2}$

$\Rightarrow | - n - 1 | = 4$

$∴$ n = 3, -5

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The number of solutions of |[x]−2x|=4 where [x] is the greatest integer is

The correct option is B 4 If x=n ϵZ, |n−2n|=4⇒n±4 If x = n + K where 0 < K < 1 then |n−2(n+k)|=4 it is possible if K=12 ⇒ |−n−1|=4 ∴ n = 3, -5

The number of solutions of $| [x] - 2 x | = 4$ where [x] is the greatest integer is

The correct option is B
4

$I f x = n ϵ Z, | n - 2 n | = 4 \Rightarrow n \pm 4$

If x = n + K where 0 < K < 1 then $| n - 2 (n + k) | = 4$ it is possible if $K = \frac{1}{2}$

$\Rightarrow | - n - 1 | = 4$

$∴$ n = 3, -5