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 POSITIVE (or zero)
therefore
-|x| is ALWAYS NEGATIVE (or zero)
|-3| = +3
|+3| = +3
so
-|-3| = -(+3) = -3
To understand the expression -|x|, let's break it down step by step.
First, let's start with |x|, which represents the absolute value of x. The absolute value is a function that returns the distance of a number from zero on the number line, regardless of its sign. So, if x is positive or zero, |x| would simply be x. For example, |3| = 3 and |0| = 0.
On the other hand, when x is negative, |x| would be equal to the positive value of x. For example, |-3| = 3 and |-5| = 5.
Now, let's consider -|x|. The negative sign in front of |x| indicates that we are taking the opposite sign of the absolute value. So, if |x| is positive, the negative sign will make it negative. And if |x| is negative, the negative sign will make it positive. Essentially, we are reversing the sign of the absolute value.
For example, if x = 4, then |x| = |4| = 4. Therefore, -|x| = -4.
On the other hand, if x = -6, then |x| = |-6| = 6. Therefore, -|x| = -6.
In summary, -|x| is equivalent to the negative of the absolute value of x.