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

Toolbox:
• Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality.
• Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality.
• If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e $'>'$ sign changes to $'<'$ and $'<'$ changes $'>'$ .
Step 1:
The given in equalities
$24 x < 100$
Dividing both sides by positive number 24 we get,
$\large\frac{24x}{24} < \frac{100}{24}$
$x < \large\frac{25}{6}$
Step 2:
The number $1,2,3,$ and $4$ are the only natural number less than $\large\frac{25}{6}$ The solution set is $\{1,2,3,4\}$
Step 3:
The integer less than $\large\frac{25}{6}$ are $-4,-3,-2,-1,0,1,2,3,4$
The solution set is $\{.......,-4,-3,-2,-1,0,1,2,3,4,\}$