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 $\{\ldots,-5,-4,-3\}$.