**Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?**

*You may wish to explore the problem* Which Is Cheaper? *before working on this task.*

Which is bigger, n+10, or 2n+3?

How did you decide?

Here’s how I decided:

But then my friend said:

Can you explain why we have come to different conclusions?

Is there a diagram you could draw that would help?

For the following pairs of expressions, can you work out when each expression is bigger?

- Find two expressions so that one is bigger whenever n<5 and the other is bigger whenever n>5.
- Find three expressions so that the first is biggest whenever n<0, the second is biggest whenever n is between 0 and 4, and the third is biggest whenever n>4.
- Find three expressions so that the first is biggest whenever n<3, the second is biggest when n>3, and the third is never the biggest.
- Find three expressions so that one of them is the biggest regardless of the value of n.

Age 14 to 16