Question

Solve $24x<100$, when (i) $x$ is a natural number. (ii) $x$ is an integer

Answer 1

$24x<100$
$\Rightarrow x<\frac{100}{24}$
$\Rightarrow x<\frac{25}{6}$
(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 $.......-3,-2,-1,0,1,2,3,4$.
Hence,in this case ,the solution set is $\{............-3,-2,-1,0,1,2,3,4\}.$