The values of x satisfying the inequality 0 -2-3-x- - 1 is in the intervalA- -1-2B- -0-2C- -1-3

The correct option is B [0,2)Given 0 ≤2/3[x] ≤ 1 Since [x] is an integer, the possible values of 2/3 [x] are 0 and 2/3, when [x] =0 or [x] = 1 respectively. W ...

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Standard XI

Mathematics

Greatest Integer Function

The values of...

Question

The values of x satisfying the inequality $0 \leq \frac{2}{3} [x] \leq 1$ is in the interval

[1,2)

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[0,2)

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[1,3)

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Solution

The correct option is B [0,2)
Given $0 \leq \frac{2}{3} [x] \leq 1$

Since [x] is an integer, the possible values of $\frac{2}{3} [x]$ are 0 and $\frac{2}{3}$ , when [x] =0 or [x] = 1 respectively.

When $[x] = 0$ , $x \in [0, 1)$
When $[x] = 1$ , $x \in [1, 2)$

Hence, the values of x for which the inequality is satisfied lie in the range [0,2)

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The values of x satisfying the inequality $0 \leq \frac{2}{3} [x] \leq 1$ is in the interval