What is the ANSWER??
If /x/ = -x, then x mst be
A. Positive
B. Nonnegative
C. Negative
D. Nonpositive
Note that is only possible if x is any real number less than or equal to zero:
x <= 0
Therefore, the answer is [D] Nonpositive.
Note nonpositive is different from negative numbers, as nonpositive includes zero, while Negative numbers does not include zero. (Zero is neither positive or negative number)
Hope this helps~ :)
Not quite.
|x| = x if x >= 0
|x| = -x if x < 0
(C)
It happens that -0 = 0, but the definition of |x| specifies that |x|=x if x>=0
To determine the value of /x/ when /x/ = -x, we can start by understanding the absolute value function. The absolute value of a number /x/ is equal to its distance from zero on the number line. Therefore, |x| is always nonnegative, meaning it is either positive or zero (0).
Now, let's substitute -x into the equation |x| = -x:
|-x| = -(-x)
To simplify the equation, we can remove the negative sign on the right side:
|x| = x
Now, we have two cases to consider:
Case 1: x is positive (x > 0)
If x is positive, then |x| = x. This satisfies the equation.
Case 2: x is zero (x = 0)
If x is zero, then |x| = 0. This also satisfies the equation.
However, if x is negative (x < 0), then |x| = -x. This does not satisfy the equation.
Therefore, based on the given equation |x| = -x, x must be either positive or zero.
The correct answer is:
A. Positive