Video Transcript
Identify whether five 𝑎 minus
three equals 22 is an expression, an equation, an identity, a formula, or an
inequality.
In order to answer this question,
we’ll need to recall what it means to have an expression, an equation, an identity,
a formula, or an inequality. Let’s begin with thinking what it
means to be an expression. An expression is a collection of
terms. So in this question, five 𝑎 minus
three would be an expression, and 22 would be an expression. As the whole statement, five 𝑎
minus three equals 22, is not an expression on its own, then we could say that this
is not an expression. There is, in fact, a mathematical
word for when we have two expressions linked by an equal sign, and that word is an
equation.
At this point, it looks as though
our statement is an equation. But let’s see if any of the other
three words would apply. Let’s take the word inequality. An inequality would, in fact, have
to have one of the inequality symbols, for example, greater than, greater than or
equal to, less than, or less than or equal to. As the statement that we’re looking
at has an equal sign, then this would not be an inequality. So what do we mean when we talk
about an identity? We can recall that an identity is
always true no matter what values the variables take. So, if we look at our statement,
will this be true no matter what the value of 𝑎 is?
Let’s say we chose the value of 𝑎
to be 100. On the left-hand side, we’d have
five times 100 minus three, which is 497, and that is not equal to 22. We, therefore, cannot say that the
statement five 𝑎 minus three equals 22 is always true. We have to say that this is not an
identity. So finally, let’s consider if this
would be a formula. We can recall that a formula is an
equality that shows how the value of a quantity depends on the value of other
quantities. It can be difficult to tell the
difference between formulas and equations because every formula will be an
equation. We can think of it somewhat
informally by thinking that a formula is like a useful equation.
For example, we might have area is
equal to length times the width, or we might have 𝐹 equals 𝑚𝑎. Usually in formulas, we’ll have at
least two variables. In the statement five 𝑎 minus
three equals 22, we just have one variable. So we don’t really see how the
value would change based on other variables. So this really just leaves us with
one answer option. We would say that five 𝑎 minus
three equals 22 is an equation. And that’s because it has that
equals to sign linking two expressions.
