91Ó°ÊÓ

The term 'multiple' refers to numbers that can be evenly divided by a specific number without leaving a remainder. For multiples of 5, we are looking at numbers like 5, 10, 15, 20, and so on. These are all results of the expression '5n', where 'n' is an integer (whole number).

To get a better grasp:

• When 'n' is 1: 5 * 1 = 5
• When 'n' is 2: 5 * 2 = 10
• When 'n' is 3: 5 * 3 = 15

Thus, the multiples of 5 form an arithmetic sequence where each term is 5 units apart from the previous one.

To solve problems like these, it's crucial to zero in on the 'range.' The range tells us the interval within which we are interested, in this case, from 7 to 79.

Identifying the range helps narrow down which multiples of 5 we need to consider. Here’s how to do it:

• Start by finding the smallest multiple of 5 greater than the lower bound (7 in this case)
• Next, find the largest multiple of 5 less than or equal to the upper bound (79)

In our example, we find that the smallest multiple of 5 greater than 7 is 10 and the largest multiple of 5 less than or equal to 79 is 75. Setting these boundaries is what allows us to create a precise and accurate solution.

Integers are whole numbers that include both positive and negative numbers as well as zero. They don’t include fractions or decimals. Examples of integers are -3, 0, 1, 5, and 10.

The traditional symbol for the set of integers is \({\mathbb{Z}}\), taken from the German word 'Zahlen,' meaning 'numbers.' When we use set-builder notation involving integers, like \({n \in \mathbb{Z}}\), we're specifying that 'n' can be any integer.

In the context of our exercise, specifying that \[ x = 5n, n \in \mathbb{Z}, 2 \leq n \leq 15 \] tells us that 'n' is an integer and must fall in the inclusive range between 2 and 15. This range ensures we cover all multiples of 5 between the numbers 10 and 75.