What's the difference between |-6| and -6 and |-8| and -|8| and |-5| and 5?

For the first one wouldn't it be = ? Both a -6

For the second one wouldn't it be < ?
-|8| bigger than |-8|

And for the last one wouldn't it be < ? 5 bigger than |-5|

Please HELP me!!!

1.The absolute value of x, denoted "|x|" is never negative. |-6| = 6.

2. -|8| = -8
|-8| = 8

3. 5 = |-5|

which one is bigger 1/2 3/5 3/4

To understand the differences between |-6| and -6, |-8| and -|8|, and |-5| and 5, let's break it down step by step:

1. |-6| and -6:
The expression |-6| represents the absolute value of -6. The absolute value of a number is its distance from zero on a number line, so |-6| equals 6 (which is positive).

On the other hand, -6 is a negative number itself. So, |-6| and -6 are different values. |-6| is positive 6, while -6 is negative 6.

Therefore, |-6| ≠ -6.

2. |-8| and -|8|:
The expression |-8| represents the absolute value of -8, which equals 8.

Now, what about -|8|? To evaluate this expression, first find the absolute value of 8, which is 8. Then, negate that result by adding a negative sign in front of it, making it -8.

So, -|8| equals -8.

Therefore, |-8| ≠ -|8|. |-8| is positive 8, while -|8| is negative 8.

3. |-5| and 5:
The expression |-5| represents the absolute value of -5, which equals 5.

At the same time, the number 5 itself is positive.

Thus, |-5| equals 5.

Therefore, |-5| = 5.

In summary:
- The absolute value of a negative number is always positive.
- The absolute value of a positive number remains the same.
- The sign of a number inside the absolute value bars does not affect the result when evaluating the bars.

Remember, to find the absolute value of a number:
- If the number is positive or zero, the absolute value is the number itself.
- If the number is negative, drop the negative sign to make it positive.

I hope this clears up the differences between these expressions for you!