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.
