when in the absolute value of x equal to the absolute value of negative x?
(always right?) negative sign is inside absolute value bars
when is the absolute value of x equal to negative absolute value?
(never?) negative sign is outside absolute value bars
always, and, on the second, when x=0.
thank you *sighs in relief*
The absolute value of a number, denoted as |x|, represents the distance of that number from zero on the number line, ignoring the sign. It is always a positive value or zero itself.
Now, let's address the two scenarios you mentioned:
1. When is the absolute value of x equal to the absolute value of negative x, where the negative sign is inside the absolute value bars?
In this case, |x| = |-x|.
To solve this, we consider that the absolute value of a number is equal to the number itself if the number is non-negative (greater than or equal to zero), and it is equal to the negative of the number if the number is negative. Therefore, |-x| = -(-x) = x. So, whenever x is non-negative, the absolute value of x is equal to the absolute value of -x.
2. When is the absolute value of x equal to negative absolute value, where the negative sign is outside the absolute value bars?
In this case, we have |x| = -|x|.
The absolute value of x is always non-negative, whereas negative numbers are always less than zero. Thus, the left-hand side of the equation (|x|) is non-negative, while the right-hand side (-|x|) is negative. Since a non-negative number cannot be equal to a negative number, the equation has no solutions. Therefore, there is never a value for x where the absolute value of x equals negative absolute value.