In mathematics, determining if a number is within a given interval is a common problem that is encountered. This article will discuss how to evaluate the number x for the interval [a,b] and verify if the number is within the interval.

## Verifying if a Number is Within an Interval

When verifying if a number is within an interval, it is important to first understand what an interval is. An interval is a set of real numbers that is bounded by two numbers, known as the endpoints. In the interval [a,b], the first number, a, is known as the lower endpoint and the second number, b, is known as the upper endpoint.

In order to verify if a number, x, is within an interval [a,b], it is necessary to first compare the number to the endpoints. If the number is greater than or equal to the lower endpoint, a, and less than or equal to the upper endpoint, b, then the number is within the interval. If the number is not greater than or equal to the lower endpoint or less than or equal to the upper endpoint, then the number is not within the interval.

## Evaluating the Number x for the Interval [a,b].

When evaluating the number x for the interval [a,b], the number must be compared to the endpoints a and b. If the number is greater than or equal to the lower endpoint, a, and less than or equal to the upper endpoint, b, then the number is within the interval. If the number is not greater than or equal to the lower endpoint or less than or equal to the upper endpoint, then the number is not within the interval.

For example, if the interval is [2,10] and the number is 8, then the number is within the interval. This is because 8 is greater than or equal to the lower endpoint, 2, and less than or equal to the upper endpoint, 10.

In conclusion, to evaluate the number x for the interval [a,b], the number must be compared to the endpoints a and b. If the number is greater than or equal to the lower endpoint, a, and less than or equal to the upper endpoint, b, then the number is within the interval.

In summary, verifying if a number is within an interval is a common problem in mathematics. To evaluate the number x for the interval [a,b], the number must be compared to the endpoints a and b.

It is often necessary to verify whether a given number is included within a specific interval. In mathematics, an interval is defined as a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. This article will discuss how to verify if a given number X is included in the interval [a,b] when three natural numbers – a, b and X – are provided.

The first step is to compare the value of X with the values of a and b. If the value of X is greater than or equal to the value of a, and it is also less than or equal to the value of b, then X is included in the interval. This can be expressed mathematically as:

X ≥ a AND X ≤ b

If both conditions from the above statement are met, then X belongs in the interval [a,b].

On the other hand, if the value of X is not greater than or equal to a, or it is not less than or equal to b, then it does not belong in the interval [a,b]. This can be expressed mathematically as:

X < a OR X > b

Both of the conditions also must be met in order for X to not belong in the interval [a,b].

In conclusion, when given three natural numbers – a, b and X – it is possible to verify if X belongs in the interval [a,b]. This can be done by comparing X with the values of a and b, and if both the conditions X ≥ a AND X ≤ b, or the conditions X < a OR X > b are met, then it can be determined whether or not X belongs to the interval [a,b].