If a set containing the element four 𝑏 is not equal to a set containing the element 44, what are the possible values of 𝑏?
The first set that’s mentioned in our problem is a set containing the element four 𝑏. Now, when we see a letter written like this, we know that this means four lots of something we don’t know, four lots of 𝑏. Let’s use this bar model to represent the first set. But what is our set worth? This is quite an interesting problem because often we’ll be given an expression like four 𝑏. And then we’ll be told what it’s equal to. And we’ll have to use that to work out what 𝑏 is worth.
But in this problem, we’re not told what four 𝑏 is equal to. We’re told what it’s not equal to. And what it’s not equal to is a set containing the element 44. So perhaps the only thing we can do with our bar model is to complete it in a way that’s not correct. Four 𝑏 does not have a value of 44. If the set was worth 44, then we could find the value of 𝑏 by dividing 44 by four. There are four lots of 𝑏 in 44. We know that 10 fours are in 40. And so there must be 11 fours in 44. And so, in this example, which we know of course is not correct, then 𝑏 would be equal to 11. Of course, we know this is not true.
So the only thing we do know about 𝑏 is that is not going to be equal to 11. This is an unusual question because we can’t give one number as an answer. The only answer that we can give is that 𝑏 can be any number except 11. If the value of 𝑏 was 11, then we know that the total value of the set would be 44. And we’re told in the question that four 𝑏 is not equal to 44. So, in a way, instead of saying what 𝑏 is worth, we’ve answered the question by saying what it’s not worth. 𝑏 can be any number except 11.