a. I am choosing an integer. I then subtract 10 from the integer, take the opposite of t...

a. I am choosing an integer. I then subtract 10 from the integer, take the opposite of the result, add , and find the opposite of the new result. My result is . What is the original number?

b. Judy wants to do the activity in part (a) with her classmates. Each classmate probably chooses a different number and Judy wants to tell each classmate quickly what number was chosen. Judy figures out that the only thing she needs to do is to add 7 to each answer she gets. Does this always work? Explain why or why not.

c. Come up with your own "trick" similar to the one in part (b) that works for each answer you get from your classmates.