Solve –12x > 30, when
Question:

Solve $-12 x>30$, when

(i) x is a natural number

(ii) x is an integer

Solution:

The given inequality is $-12 x>30$.

$-12 x>30$

$\Rightarrow \frac{-12 x}{-12}<\frac{30}{-12} \quad$ [Dividing both sides by same negative number]

$\Rightarrow x<-\frac{5}{2}$

(i) There is no natural number less than $\left(-\frac{5}{2}\right)$.

Thus, when x is a natural number, there is no solution of the given inequality.

(ii) The integers less than $\left(-\frac{5}{2}\right)$ are …, $-5,-4,-3$.

Thus, when x is an integer, the solutions of the given inequality are

$\ldots,-5,-4,-3$

Hence, in this case, the solution set is $\{\ldots,-5,-4,-3\}$.