Given:
Secret number is more than 11 units away from 50.
To find:
The absolute- value inequality that gives the possible values of Mai's number.
Solution:
Let the secret number be x.
Secret number is more than 11 units away from 50. It may be less than 50 or more than 50.
Case 1: If x<50, then [tex]50-x>11[/tex]
Case 2: If x>50, then [tex]x-50>11[/tex]
It means the absolute difference between secret number and 50 is greater than 11.
[tex]|x-50|>11[/tex]
Therefore, the required inequality is [tex]|x-50|>11[/tex].
