Question

YOUR ASSIGNMENT: Difference of 10 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. Your Player 1. Choose your player, and record the number chosen by the other player. (2 points: 1 point for each answer) a. Which player did you select

Answer 1

`|x - y| > 10` ---- Nita wins

`|x - y| < 10` --- Eric wins

Explanation:

The complete instruction is to determine the range at which Erik or Nita wins.

To start with, let

`x \to` Erik's score

`y \to` Nita's score

If the difference is greater than 10, the Nita wins.

This implies that:

`|x - y| > 10` ---- Nita

If less than 10, then Eric wins

This implies that:

`|x - y| < 10` --- Eric wins

Now, assume that Nita chose 5.

For Nita to win, we have:

`|x - y| > 10`

`|x - 5| > 10`

Remove the absolute symbol

`-10 > x - 5 > 10`

Split

`-10 > x - 5\ or\ x - 5 > 10`

Solve for x

`5 -10 > x \ or\ x > 10 + 5`

`-5> x \ or\ x > 15`

Rewrite as:

`x< -5 \ or\ x > 15`

x cannot be negative.

So:

`x > 15`

x cannot exceed 20.

So:

`15 < x \le 20`