# Question Video: Completing a Phrase About the Language of Algebra Mathematics

Fill in the blank: ＿ is an equation that is always true, no matter what values are chosen.

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### Video Transcript

Fill in the blank. What is an equation that is always true, no matter what values are chosen.

Let’s begin by recalling what we mean by an equation. The important thing about an equation is that it has the equals to symbol. It will have an expression on the left-hand side and one on the right-hand side. So we could, for example, have an equation like six 𝑥 plus one equals 13. So what do we mean by an equation that’s always true no matter what values are chosen? We could see in the equation that we’ve chosen that this wouldn’t always be true. We could solve this to see that the value of 𝑥 must be two, as six times two plus one would give us 13. So this would not be a good example of an equation that’s always true.

If we wrote an equation like 0.1𝑥 equals 𝑥 over 10, then this would actually always be true. We could choose any value of 𝑥, and the left-hand side would always be equal to the right-hand side. There is, in fact, a special word for an equation that’s always true no matter what values are chosen, and that’s identity. Therefore, our answer would be an identity.