An expression for Florence's new number, y, is: y = 4x + 14
we can factor out a 2 from the expression: y = 4x + 14 = 2(2x + 7)
Florence thinks of a number, x. She then multiplies it by 4 and adds 14. We can write this as an expression: y = 4x + 14
In the given image, Florence thinks of a whole number, x, and then multiplies it by 4 and adds 14. This can be represented by the following expression:
y = 4x + 14
where y is the new number that Florence calls y.
This expression can be factored as follows:
y = 2(2x + 7)
This means that y is a multiple of 2, because it can be divided by 2.
In other words, any number that Florence thinks of, x, will always result in a new number, y, that is a multiple of 2. This is because the expression 4x + 14 is always a multiple of 2.
Here is an example:
If Florence thinks of the number 5, then her new number, y, will be:
y = 4(5) + 14 = 34
34 is a multiple of 2 because it can be divided by 2 evenly.
If Florence thinks of the number 10, then her new number, y, will be:
y = 4(10) + 14 = 54
54 is also a multiple of 2 because it can be divided by 2 evenly.
Therefore, we can conclude that Florence's new number, y, is always a multiple of 2, regardless of the number that she chooses for x.