Question

Find the number of elements of $\times$ which satisfy the inequation

$-2\le \left(\frac{1}{2}\right)-\left(\frac{2x}{3}\right)\le 1\left(\frac{5}{6}\right),xϵN$

• A. 4
• B. 3
• C. 5
• D. None of these

Answer 1

The correct option is B

3

We have,

$-2\le \left(\frac{1}{2}\right)-\left(\frac{2x}{3}\right)\le 1\left(\frac{5}{6}\right)$

$\Rightarrow -2\le \left(\frac{1}{2}\right)-\left(\frac{2x}{3}\right)\le \left(\frac{11}{6}\right)$

$\Rightarrow -12\le 3-4x\le 11$

$\Rightarrow -12-3\le 3-4x-3\le 11-3$

$\Rightarrow -15\le -4x\le 8$

$\Rightarrow 15\ge 4x\ge -8$

$\Rightarrow -8\le 4x\le 15$

$\Rightarrow -2\le x\le \left(\frac{15}{4}\right)$

$\Rightarrow -2\le x\le 3\left(\frac{3}{4}\right)$ [Dividing throuhghout by 4]

But, x $ϵ$ N , i.e x $ϵ$ {1,2,3,4,….}

So, the solution set is {1,2,3}.