Question

Mai thinks of a secret number. She says that her secret number is more than 11 units away from 50. Write an absolute- value inequality that gives the possible values of Mai's number.

Answer 1

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 $50-x>11$

Case 2: If x>50, then $x-50>11$

It means the absolute difference between secret number and 50 is greater than 11.

$|x-50|>11$

Therefore, the required inequality is $|x-50|>11$.