True or False and why:
|-x| = x, x<0
false. the left side is = positive, regardless of x value. Right side is positive only if x>0.
| - x |² = x²
x = ± √ x²
x = ± x
| x |² = x²
x = ± √ x²
x = ± x
This mean | - x | = | x |
For x < 0
| - x | = | x |
| - x | < 0
For x > 0
| - x | = x
| - x | > 0
False.
@Bosnian & @bobpursley
Thank you so much for the help. I really appreciate it because I am kind of struggling with Absolute Values.
False.
The absolute value of a negative number is always positive. So, in the case where x < 0, the absolute value of x, denoted as |-x|, will always be the opposite of x.
For example, if x = -3, then |-x| would be |-(-3)| = 3, which is positive. Similarly, if x = -7, then |-x| would be |-(-7)| = 7.
Therefore, for x < 0, the absolute value of x, |-x|, is not equal to x, but rather equal to the opposite of x.