Question

Find the values of x, which satisfy the inequation:

$2\le \frac{1}{2}-\frac{2x}{3}\le \frac{11}{6}$ , x $ϵ$ N.

• A. 2
• B. 3
• C. 4
• D. 1

Answer 1

The correct option is B

3

We have,

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

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

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

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

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

$15\ge 4x\ge -8$

$-8\le 4x\le 15$

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

$-2\le x\le 3\left(\frac{3}{4}\right)$

But, $xϵN$ , i.e $xϵ${1,2,3,4,….}

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