Question

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

Answer 1

Hint: Since to solve the given problem we need to know about the concept of division and less than symbol or inequality.
The process of the inverse of the multiplication method is called division. Like $x \times y = z$ is multiplication thus the division sees as $x = \dfrac{z}{y}$. Like $x = \dfrac{{10}}{5} = 2$ which is the remainder value.
Less than inequality is the symbol represented as $ < $ which means the left-side entries or numbers are less variable than the right-side entries like $1 < 2$ where one is less than two.

Complete step by step answer:
Since given that the equation as $24x < 100$
Now by applying the division operation and divide both of the values with the number $24$ then we get $\dfrac{{24x}}{{24}} < \dfrac{{100}}{{24}}$
Now canceling the common terms we get $x < \dfrac{{25}}{6}$ and then we have the decimal value as $x < 4.16$ which is not in the form of integers or natural numbers because it is a rational number as expressed as $\dfrac{p}{q}$ the format.
(i) when x is a natural number.
Suppose the x is a natural number, which means natural numbers can be expressed in the form of $1,2,3,4,....\infty $ then we get $x < 4.16$ as $1,2,3,4$ because after four we get the number $5$ which is greater than that we found.
Thus, the value of x as the natural number is $1,2,3,4$
(ii) when x is an integer.
Suppose the given x is an integer then by the integer definition we have $( - \infty ,\infty )$ which means there is no end at positive and negative values and then we have $\{ ....., - 3, - 2, - 1,0,1,2,3,.....\} $
Thus, the value of x as integers is $\{ ..., - 3, - 2, - 1,0,1,2,3,4\} $ after four which is a greater value.

Note:
The natural numbers are the numbers starting from one and there is no end also there are only positive terms like $1,2,3,4,....\infty $
The whole numbers are natural numbers and contain also zero, thus we have $0,1,2,3,4,....\infty $
The integers are whole numbers and contain the negative sign values also thus we have $ - \infty ,....., - 3, - 2, - 1,01,2,3,4,....\infty $
We make use of the general mathematical terms to solve the given problem easily.