The sum of the opposite of a number and the absolute value of the number is equal to the number itself. True,sometimes true,or never true?

say the number is +2

-2 + |2| = 0 which is not 2

say the number is -2
+2 +|-2| = 4 which is not true

say the number is +zero
-zero + |zero| = zero

so sometimes (if zero :)

To determine if the statement is true, sometimes true, or never true, let's break it down step by step.

The sum of the opposite of a number and the absolute value of the number is equal to the number itself. In mathematical terms, we can express this as:

(-x) + |x| = x

Where x is a number.

Now let's consider different cases:

1. If x is a positive number:
In this case, the opposite of x would be -x and the absolute value of x would also be x. Substituting these values into the equation, we get:
(-x) + x = x
This simplifies to:
0 = x

Since x is positive and 0 is not positive, the equation does not hold true in this case.

2. If x is zero:
When x is zero, the opposite of x (-x) is still zero and the absolute value of x (|x|) is also zero. Substituting these values, we get:
0 + 0 = 0
This equation is true when x is zero.

3. If x is a negative number:
In this case, the opposite of x would be -x and the absolute value of x (-x) would be -x as well. Substituting these values, we get:
(-x) + (-x) = x
This simplifies to:
-2x = x

Now, if we divide both sides of the equation by x, we get:
-2 = 1

Since -2 is not equal to 1, the equation does not hold true in this case either.

Therefore, based on the above analysis, we can conclude that the statement is NEVER TRUE.