Question

Solve the following inequation and find the cardinality of the solution set.

$\frac{2x+3}{3}\ge \frac{3x-1}{4}$ where x is positive even integer.

Answer 1

We have
$\frac{2x+3}{3}\ge \frac{3x-1}{4}$

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

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 = 7