shouldn't it be x and x[-1] because the delay outputs a number with a smaller index in the series? I actually would prefer the comnventional x[n] and x[n-1] but I see that 0 and 1/-1 is easier. Just saying because you introduce(really nicely) some of the "scary" vocabulary and this is also a very typical one.
To calculate the average of a set of numbers you add all of the numbers together and then divide the result by how many numbers there are. So to average two numbers we add them together and divide by 2 -- which is the same as adding two numbers together and multiplying by 0.5 -- which is also the same as multiplying each of the numbers by 0.5 first and then adding them together.
Hopefully that helps! Lots of ways to re-write the same basic math equations :-)