Question

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 is greater than 10, then Nita wins. Use what you know about inequalities and absolute values to better understand the game.

Answer 1

Interesting question. Have you tried playing it yourself to get a feel for it?

Answer 2

I need to write an inequality, defining my variables and graph it to find solution set.

Answer 3

Yes. I am stumped I chose Erik as my player. The other player chose 8.

Answer 4

So if Erik wants to win we just pick anything within 10 of 8, so we can only lose by picking 19 or 20

Answer 5

That is a good choice. If you were eric what number would you want to choose?

Answer 6

Maybe something like... |x-8| <10 ?

Answer 7

That seems to work. Let's test it.

Answer 8

Oops. Guess my first instinct was wrong, he will also lose if he picks 18.

Answer 9

Would this be a valid inequality for the question?

Answer 10

Perhaps, the problem is... we have only tested one value for Nita = 8.

Answer 11

You are right! Nobody wins if he picks 18!

Answer 12

Interesting... a tie game is possible!

Answer 13

I think I have enough information to complete this assignment now. Thank you! I was making much more complicated than it needs to be!

Answer 14

OK, good luck. I would just add, perhaps consider calling Nita's choice N or y instead of just 8. That will give you all possibilities. Good luck!

Answer 15

Yes I tried that. But then I was not able to graph it.... I don't now how to graph |x-y| <10

Answer 16

OK, well, this is a double inequality. Think of the x-y as one number. In order for the absolute value to be less than 10, this number must be between -10 and +10. In other words:

-10 < x-y < 10

Answer 17

Or sometimes people like separating the inequality to make it easier
1) -10 < x-y
2) x-y < 10

By solving for y you will get two inequality graphs.

Answer 18

Not sure if your class has covered this yet, or if this is kind of a warm up exercise. :)

Answer 19

Aren't the two lines parallel?

Answer 20

Let's see:
1) y < x + 10
2) y > x - 10

They are parallel, but remember to fill in above and below each line as needed.

Answer 21

Something like this.