Video Transcript
For what value of 𝑛 is the modulus or absolute value of 𝑛 minus two plus two equal to zero?
So the first thing we need to consider is the absolute value or modulus of 𝑛 minus two and what does this mean. Well, the absolute value of a number can sometimes be thought of as its distance from zero. And what that means in practice is that the absolute value or modulus of 𝑛 minus two is the nonnegative value of 𝑛 minus two without us thinking about the sign. So therefore, we can consider the modulus or absolute value of 𝑛 minus two as a positive value.
So let’s think about what the question is asking. It’s asking us to say what value of 𝑛 is the modulus of 𝑛 minus two plus two equal to zero. So if we think about that, we’ve got a positive because we know that the modulus of 𝑛 minus two is positive plus two needs to be equal to zero. But it cannot be because a positive plus another positive cannot be equal to zero. Therefore, we can say that there is no such value of 𝑛. And I’m just gonna quickly demonstrate why.
Well, if 𝑛 was equal to zero, then 𝑛 minus two would be equal to negative two. So we could think, well, that would be negative two plus two. Well, that will be equal to zero. However, the modulus or absolute value of negative two is going to be two because we said that it has to be a positive value.
And therefore, if we had two plus two, this would be equal to four. So it would not be equal to zero.
