Video: Identifying Using the Language of Algebra

Identify whether 5𝑎 − 3 = 22 is an expression, an equation, an identity, a formula, or an inequality.

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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.

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