The question is: You plan on attending a picnic for the up coming holiday. You can either go to your sister's picnic who lives 10 miles west of your house or to your friends picnic who lives 10 miles east of your house. write an absolute value inequality that represents all the distances you may be from your house.
|x-?|= 10
so to me the question mark should be 20.
Actually, the question mark should be 0 since your house is considered the reference point. The absolute value inequality representing all the distances you may be from your house is:
|x-0| = 10
This simplifies to:
|x| = 10
To represent all the distances you may be from your house, you can use the absolute value inequality:
|x - 0| ≤ 10
This inequality states that the distance (represented by |x - 0|) from your house (0) must be less than or equal to 10. This means you can be up to 10 miles away from your house in either direction.
To find the value that should replace the question mark in the absolute value inequality |x - ?| = 10, let's analyze the situation.
You have two options for the picnic: your sister's picnic, which is 10 miles west of your house, or your friend's picnic, which is 10 miles east of your house. Since distance is always positive, we can use the absolute value to represent the absolute distance from your house.
Let's consider the distances:
1. If you go to your sister's picnic, you will be 10 miles west of your house. In this case, the absolute distance from your house is |x - (-10)| = |x + 10|.
2. If you go to your friend's picnic, you will be 10 miles east of your house. In this case, the absolute distance from your house is |x - 10|.
To represent all possible distances you may be from your house, we need to consider both scenarios. Therefore, the correct absolute value inequality is:
|x + 10| = 10 or |x - 10| = 10.
This inequality represents all the distances you may be from your house, considering both options for the picnic.