Question

Erik and Nita are playing a game with numbers. In the game, they each think of a random number from 0 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 the information in the interactive and what you know about absolute value inequalities to better understand the game.

Answer 1

Question:

Write an algebraic statement that represents all the ways your player will win. Be sure to define your variable

Answer:

Erica:

`0 \leq |x - y| < 10`

Nita:

`10 < |x - y| \leq 20`

Explanation:

Given

Players: Erica & Nita

Range: 0 to 20

Represent Erica with x and Nita with y

For Erica to win;

The difference between x and y must be less than 10 but greater than or equal to 0

i.e.

`0 \leq x - y \leq 10` or
`0 \leq y - x \leq 10`

These two expressions can be merged together to be:

`0 \leq |x - y| < 10`

For Nita to win;

The difference between x and y must be greater than 10 but less than or equal to 20

i.e.

`10 < x - y \leq 20` or
`10 < y - x \leq 20`

These two expressions can be merged together to be:

`10 < |x - y| \leq 20`