Question

Solve 24x < 100, when (i) x is a natural number (ii) x is an integer. Please answer it fast

Answer 1

Solution :-

The given inequality is 24x < 100.

$\rm{24x<100}$

Divide both sign by  same positive number

$\Rightarrow \rm{\dfrac{24x}{24}<\dfrac{100}{24}}$K

$\Rightarrow \rm{x<\dfrac{25}{6}}$

1) It is evident that 1, 2, 3, and 4 are the only natural numbers less than $\rm{\dfrac{25}{6}}$

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}.

2) The integers less than  $\rm{\dfrac{25}{6}$ 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}.