Question:
Solve 24x < 100, when
(i) x is a natural number
(ii) $x$ is an integer
Solution:
The given inequality is $24 x<100$.
$24 x<100$
$\Rightarrow \frac{24 x}{24}<\frac{100}{24}$ [Dividing both sides by same positive number]
(i) It is evident that $1,2,3$, and 4 are the only natural numbers less than $\frac{25}{6}$
Thus, when x is a natural number, the solutions of the given inequality are 1, 2, 3, and 4.
Hence, in this case, the solution set is {1, 2, 3, 4}.
(ii) The integers less than $\frac{25}{6}$ are ...-3, $-2,-1,0,1,2,3,4$.
Thus, when x is an integer, the solutions of the given inequality are
…–3, –2, –1, 0, 1, 2, 3, 4.
Hence, in this case, the solution set is {…–3, –2, –1, 0, 1, 2, 3, 4}.