Write each of the following expressions without using the absolute value sign.
|x−4| if x>4
since |v| = v if v>0
|x-4| = x-4 if x>4
What is the answer?
x-4
To remove the absolute value sign in the expression |x-4| when x > 4, we need to consider two cases:
1. When x > 4, the expression inside the absolute value sign becomes (x-4). So the equivalent expression would be (x-4).
2. When x <= 4, the expression inside the absolute value sign becomes -(x-4) since the absolute value of a negative number is the positive value of that number. So the equivalent expression would be -(x-4).
Combining both cases, the expression without using the absolute value sign for |x-4| if x > 4 is:
For x > 4: (x-4)
For x <= 4: -(x-4)