Answer:
-(x-120)
x-(-12)
-(x-(-12))
0
x / 3
-(x/3)
0
Step-by-step explanation:
1. || x-120||, if x<-120.
If x is less than -120, then x - 120 will be a negative number.
Since absolute value will make a negative number positive, the answer will be -(x-120).
2. ||x-(-12)||, if x > -12.
Basically x -(-12) = x + 12. If x is greater than -12, then ||x+12|| will be positive. The answer is x-(-12).
3. ||x-(-12)||, if x < -12.
Again, x-(-12) = x + 12. If x is less than -12, ||x+12|| will be negative.
Absolute value makes a negative number positive. The answer is -(x-(-12)).
4. ||x-(-12)||, if x = -12.
So we can substitute x with -12. ||-12-(-12)|| = ||-12+12||, which equals ||0||, which is also just 0. (Answer is 0.)
5. ||x / 3||, if x > 0.
Any positive number divided by another positive number will be positive, meaning you can just take out the absolute value sign. Answer is x /3.
6. ||x / 3||, if x < 0.
Any number less than 0 is negative, and any negative number divided by a positive number will be negative. If we take out the absolute value, we'll have to reverse it with a -. Answer: -(x/3).
7. ||x / 3||, if x = 0.
||0/3|| = ||0||, which is still 0.
Hope this helps!
