How many integers satisfy the condition 0 -2-3-x-1

[x] takes only integer values. 0 ≤2/3[x]≤1 ⇒ 0 ≤[x]≤1.5 nbsp; nbsp; nbsp; So the values nbsp;[x] can assume are 0 and 1. Therefore, the integral solut ...

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Standard XII

Mathematics

Greatest Integer Function

How many inte...

Question

How many integers satisfy the condition $0 \leq \frac{2}{3} [x] \leq 1$

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Solution

[x] takes only integer values.
$0 \leq \frac{2}{3} [x] \leq 1$
$\Rightarrow 0 \leq [x] \leq 1.5$

So the values [x] can assume are 0 and 1.

Therefore, the integral solutions for this inequality are 0, 1

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[x] takes only integer values. 0≤23[x]≤1 ⇒0≤[x]≤1.5 So the values [x] can assume are 0 and 1. Therefore, the integral solutions for this inequality are 0, 1

How many integers satisfy the condition $0 \leq \frac{2}{3} [x] \leq 1$

__

[x] takes only integer values.
$0 \leq \frac{2}{3} [x] \leq 1$
$\Rightarrow 0 \leq [x] \leq 1.5$

So the values [x] can assume are 0 and 1.

Therefore, the integral solutions for this inequality are 0, 1