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

Let X is the random number Erik thinks of, and Y is the random number Nita thinks of.
Both X and Y are in the range from 0 to 20.
X<=20
Y<=20
If the difference between their two numbers is less than 10, then Erik wins.
The difference between the two numbers can be written X-Y, or Y-X depending on which number (X or Y) is greater. But we do not know that. In order not to get negative value, we calculate absolute value of X-Y,  written |X-Y| which will give positive value whether X is greater than Y or not.
If |X-Y|<10 Erik wins.
If the difference between their two numbers is greater than 10, then Nita wins. 
If |X-Y|>10 Nita Wins