I need help with this algebraic word problem. It involves inequalities and possibly absolute value.

Question

erik and nita are playing a game. They both choose a number between 0 and 20. If the difference of their numbers is less than 10, Erik wins. If the difference is more than ten, Nita wins. Write an algabraic statement that represents all the ways each player can win.

Answer 1

x=Erik's number

y=Nita's number

 

Use absolute value to evaluate the difference(or distance between the numbers).  The distance between 2 numbers is a positive number.

 

Then use your inequalities to determine the winner.

Less than 10 Erik wins:

|x-y|<10

Greater than 10 Nita wins:

|x-y|>10