Answer:
|x - 4|
Explanation:
Let's say that the distance that Aisha bikes after school each day is represented by the variable "x". We want to write an absolute value equation that represents the distance that Aisha bikes, given that Carlos lives 1 mile further along the path.
If Aisha bikes directly home, then the distance she bikes is just the distance from school to her home, which is 3 miles. If she bikes all the way to Carlos' place before going home, then the distance she bikes is the total distance from school to Carlos' place and then from Carlos' place to her home. This total distance is equal to:
|x - (3 + 1)|
where "x - (3 + 1)" represents the distance from school to Carlos' place (which is equal to the distance that Aisha bikes beyond her home), and the absolute value symbols ensure that the expression inside the absolute value is positive.
Therefore, the absolute value equation that represents the distance that Aisha bikes after school each day is:
|x - 4|
P.S - Sorry if this is too wordy