Final answer:
The set includes all numbers from 5 to 7, inclusive, represented by the inequality 5 ≤ x ≤ 7 or the interval notation [5, 7].
Step-by-step explanation:
The set of all numbers greater than or equal to 5 and less than or equal to 7 is expressed using inequality notation as 5 ≤ x ≤ 7.
This means that any number 'x' that is 5, any number greater than 5, and all numbers up to and including 7 belong to this set.
In mathematical terms, we can describe this set on a number line where it includes all the numbers between and including the endpoints 5 and 7.
For example, numbers like 5.1, 6, 6.5, and 7 are all in this set.
The numbers that are outside of this range, such as 4.9 or 7.1, do not belong to the set since 4.9 is less than 5 and 7.1 is greater than 7.
This range is sometimes referred to as a closed interval because it includes its endpoints, shown by the square brackets in interval notation: [5, 7].