Question

If $\frac{2x+3}{3}\ge \frac{3x-1}{4}$ (where x is positive even integer), then the cardinality of the solution set is .

• A. 6
• B. 7
• C. 8
• D. 5

Answer 1

The correct option is B 7

We have,

4 (2x + 3) $\ge$ 3 (3x - 1)

8x + 12 $\ge$ 9x – 3

15 $\ge$ x

$\therefore$ x $\le$ 15

So, x $ϵ${2, 4, 6, 8, 10, 12, 14}

Hence the cardinality of the solution set, n(S) = 7.