You plan on going golfing this weekend with a friend. You can either go to your favorite course which is 14 miles north of your house or to your friend's favorite course which is 14 miles south of your house. Write an aboe value inequality that represents all the distances you may be from your house.

x≤14

To write an absolute value inequality that represents all the distances you may be from your house, we can use the concept of absolute value. The absolute value of a number represents its distance from zero on a number line.

In this scenario, the distances you can be from your house can either be north (positive) or south (negative) of your house. Let's use the variable 'x' to represent the distance from your house.

Since your favorite course is 14 miles north of your house, the distance from your house would be positive 14 miles, so we can write this as x > 14.

On the other hand, since your friend's favorite course is 14 miles south of your house, the distance from your house would be negative 14 miles, so we can write this as x < -14.

Combining these two conditions, we get the absolute value inequality:

|x| > 14

This inequality states that the absolute value of x, which represents the distance from your house, is greater than 14.