Based on what we established about the classification of x and using the closure of integers, what does the equation tell you ab
out the type of number x must be for the sum to be rational? What conclusion can you now make about the result of adding a rational and an irrational number?
Answer: The product of a rational number with an irrational number is an irrational number. To see this assume that x is a rational number and y an irrational number. Then let us assume that the product xy is rational, which means that there are integers a,b such that xy=a/b. But then we obtain y=(1/x)(a/b) which is also rational since the set of rational numbers is closed under multiplication. But this is a contradiction since y was assumed to be an irrational number.
In my opinion the following statement would be true. In order to become good at anything you need to practice, (also could mean hard work) and determination the drive to get good at the act you are working on. Some believe discipline would often be a good way to get good at something.
