# Why you can you do n-12 but not 12-n?

The subtraction is not commutative, it means that n - 12 is not the same as 12 - n, except when n is 12. For example, suppose that we have a statement such as n - 12 = 12 - n. Can we find a value for n which will satisfy our statement?

n - 12 = 12 - n (add n and 12 to both sides)

n

2n = 24 (divide by 2 both sides)

n = 12

Check:

n - 12 = 12 - n

12 - 12 =? 12 - 12

0 = 0 True

But, for all other values of n, the statement is not true. Let's say that n = 20

Does 20 satisfies the statement? Check:

n - 12 = 12 - n

20 - 12 =? 12 - 20

8 = -8 False

Hence, we cannot write n - 12 as 12 - n for n ≠12.

n - 12 = 12 - n (add n and 12 to both sides)

n

**+ n**- 12**+ 12**= 12**+ 12**- n**+ n**2n = 24 (divide by 2 both sides)

n = 12

Check:

n - 12 = 12 - n

12 - 12 =? 12 - 12

0 = 0 True

But, for all other values of n, the statement is not true. Let's say that n = 20

Does 20 satisfies the statement? Check:

n - 12 = 12 - n

20 - 12 =? 12 - 20

8 = -8 False

Hence, we cannot write n - 12 as 12 - n for n ≠12.