Question

Solve the inequation 3 $\ge$ $\frac{(x-2)}{2}$ + $\frac{x}{3}$, x $\in$ N. Find the cardinality(number of elements) of the set representing all the possible values of x.

• A. 10
• B. 8
• C. 4
• D. 5

Answer 1

The correct option is C

4

3 $\ge$ $\frac{(x-2)}{2}+\frac{x}{3}$

or 3 $\ge$ $\frac{\left[3\right(x-2)+2x]}{6}$

or 3 $\ge$ $\frac{(3x-6+2x)}{6}$

or 3 $\ge$ $\frac{(5x-6)}{6}$

Multiplying both sides by 6, we get:

6 × 3 $\ge$ $6\left[\frac{(5x-6)}{6}\right]$

or 18 $\ge$ 5x-6

or 18+6 $\ge$ 5x

or 24 $\ge$ 5x

or x $\le$ 4.8

Since x $\in$ N, x = {1, 2, 3, 4}.

So, the cardinality of the set is 4.