Question

Solve the following expression 24x < 100, when (i) x is a natural number.

Answer 1

Hint: Proceed the solution of this question first by solving the expression as given in the question then find the possible values of x according to the definition of natural number.

Complete step-by-step answer:
In the question it is given that
⇒24x < 100
So on dividing by 24 on both sides
⇒${\text{x < }}\dfrac{{{\text{100}}}}{{24}}$
So on reducing the fraction
​⇒${\text{x < }}\dfrac{{25}}{6} \Rightarrow {\text{x < 4}}{\text{.167}}$
We know that
Natural numbers are a part of the number system which includes all the positive integers from 1 till infinity. It is an integer which is always greater than zero (0). Natural numbers are countable and are generally used for calculation purposes. These are represented by the letter “N”.
As in question it is given that x is a natural number so,
Hence it is clear that 1,2,3 and 4 are the only natural numbers less than 4.167​,
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}.

Note: In this particular question we should know that Natural numbers will never consist of negative numbers and zero. These include only the positive integers i.e. set of all the counting numbers like 1, 2, 3, ………. excluding all the fractions, decimals, and negative numbers. Natural numbers are part of real numbers. We can say all natural numbers are real numbers but vice versa not true.