Question

Is this equation an identity?

k - 4 = 4 + k

Yes or No

Answer 1

no

Explanation:

An identity is an equality that is always true. An equation is an equality that is (only necessarily) conditionally true.

That is to say that for any real value inputted into a variable in an identity, an equality will result, whereas only certain values for a variable in an equation will necessarily result in an equality.

If the given equation is an identity, it should result in an equality no matter what the input for k is. So, to prove that it isn't an identity, we simply have to find one value for k that results in an inequality. To do so, we can simply plug in 0 for k and simplify.

`k - 4 = 4 + k`

`0 - 4 \stackrel{?}{=} 4 + 0`

`-4 \\e 4`

We have found one value for k that results in an inequality. Thus, this equation is not an identity.