Question

If $x$ is a prime number, then the solution set of the inequation
$\frac{x}{3}-2\ge \frac{x}{2}-5\text{is:}$

[1 Mark]

• A. x={2, 3, 5}
• B. x={2, 3, 5, 7}
• C. x={2, 3, 5, 7, 11, 13}
• D. x={2, 3, 5, 7, 11, 13, 17}

Answer 1

The correct option is D x={2, 3, 5, 7, 11, 13, 17}

Given,
$\frac{x}{3}-2\ge \frac{x}{2}-5$
where $x$ is a prime number
$\Rightarrow \frac{x}{3}-\frac{x}{2}\ge 2-5$
$\Rightarrow \frac{2x-3x}{6}\ge -3$
$\Rightarrow \frac{-x}{6}\ge -3$
$\Rightarrow \frac{x}{6}\le 3$
$\Rightarrow x\le 18$
$\text{Since x is a prime number,}$
$\therefore x=\left\{2,3,5,7,11,13,17\right\}$