I am working with absolute value. I understand this concept for
|x| When x= Greater or equal to 0
|-x| when x= less than 0
Now I don’t understand this below.
-|x|
Please help. Thank you!
|x| is always greater than 0 , to the right of the origin on number line.(or equal to zero)
therefore
-|x| is always to the left of zero (or zero)
-|x| </= 0
by the way |-x| = |x| >/= 0
It is always positive or zero
One way to think:
| of point on number line| = length of string from origin to the point. It could be left or right, same string length.
- the string length is negative :)
To understand the expression -|x|, we need to break it down into two separate parts:
1. The absolute value of x, denoted as |x|, is the non-negative value of x, regardless of its sign. In other words, it gives the distance of x from 0 on the number line. For example, |5| = 5 and |-5| = 5.
2. The negative sign, denoted as -, changes the sign of the value it is applied to. For example, -5 changes the positive 5 to negative -5, and -(-5) changes the negative -5 back to positive 5.
Now, putting these two parts together, -|x| means that we first take the absolute value of x, and then change its sign to become negative. So, if x is a positive number, like x = 5, then -|x| would be -|5| = -5. Similarly, if x is a negative number, like x = -5, then -|x| would be -|-5| = -5.
In summary, the expression -|x| negates the absolute value of x, resulting in a negative value.