# Solving Inequalities

Erik and Nita are playing a game with numbers. In the game, they each think of a random number from zero to 20. If the difference between their two numbers is less than 10, then Erik wins. If the difference between their two numbers to greater than 10, then Nita wins. Use what you know about inequalities and absolute values to better understand the game.

1. a) Which player did you select?
1. b) What number did the other player pick?
2. Should you use an equation or an inequality to represent the ways your player can win. Explain why.
3. If Erik had a 4 and Nita had a 12, would the winner be different if Nita got the 4 and Erik got the 12?
4. Is it appropriate to use an absolute value function to represent how people win this game? Why?
5. If your player is Erik, write an expression that shows all of the ways that Erik will if Nita chooses 7. If your player is Nita, write an expression that shows all of the ways that Nita will win if Erik chooses 17 (be sure to define your variables)
6. In order to graph your solution, solve for the variable. Be sure to show your work.
7. Sketch a graph of your solution.
8. What is the range of numbers that will win the game for your player. If your player is Erik, assume that Nita chooses 7. If your player is Nita, assume that Erik chooses 17.
9. Graph all the possible numbers that your player could pick. Compare this graph to your answer in question 8. If your player is Erik, and Nita chooses 7, does Erik have a good chance of winning? If your player is Nita, and Erik chooses 17, does Nita have a good chance of winning?

I honestly don't know how to do this, any help would be greatly appeciated. :)

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