Suppose that n is an integer such that n/3 is 12 greater than n/2. Which of the following is the value of n?

You said that n/3 = n/2 + 12.

There's only one number that 'n' can be.

It may or may not be an integer. We'll have to see.

Subtract n/2 from each side: n/3 - n/2 = 12

Multiply each side by 12 : 4n - 6n = 144

Do the subtraction on the left: - 2n = 144

Divide each side by - 2 : n = - 72

Yep. It turns out that 'n' is an integer.

It didn't have to be, just because you said so.

For example, if you said that n/3 is only

11 greater than n/2, we could figure out

what number 'n' must be, and it wouldn't

be an integer.