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 ...

You visited us 5 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

[0,2)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

[1,3)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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)

Suggest Corrections

Similar questions

The roots of the equation $3^{2 x} - {10.3}^{x} + 9 = 0$ are

Q. The set of values of

x,

satisfying the inequality

∣ ∣ ∣ \frac{1}{| x | - 3} ∣ ∣ ∣ > \frac{1}{2}

Q. The inequality

(x - 3 m) (x - m - 3) < 0

is satisfied for x in

[1, 3]

. Determine the values of m for this to hold good.

Q. The set of values of

a

for which the inequality,

(x - 3 a) (x - a - 3) > 0

is satisfied for all

x ε [1, 3]

Q. If

x

satisfies the inequality

{log}_{x + 3} (x^{2} - x) < 1,

then

Join BYJU'S Learning Program

The values of x satisfying the inequality 0≤23[x]≤1 is in the interval

The correct option is B [0,2)Given 0≤23[x]≤1 Since [x] is an integer, the possible values of 23[x] are 0 and 23, when [x] =0 or [x] = 1 respectively. When [x]=0, x∈[0,1) When [x]=1, x∈[1,2) Hence, the values of x for which the inequality is satisfied lie in the range [0,2)

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